able to escape the consequences by doing so.

Finally, Coleridge's use of the word "fiend" foreshadows Victor's view of his creature.  He often uses the term to describe the monster, ignoring the fiend within himself.

When Mary Shelley was 8 years old, she heard Samuel Coleridge recite "The Rime of the Ancient Mariner" in her parent's home. Mary Shelley was heavily influenced by the poetry of Coleridge, and Frankenstein is rich with allusions to "Rime of the Ancient Mariner." This excerpt from the poem parallels Victor's mood and actions. At this point, Victor is wandering the streets alone, contemplating the deaths of William and Justine, and his implicit guilt.  Of course, the shadow of his creation in constantly haunting him, and may well be following him down the road in this moment.

In the Gothic sense, Victor relates to the Mariner’s isolation and fear. In the Romantic sense, both the Mariner and Victor want the knowledge; however, unlike the Mariner, Victor’s new knowledge brings a curse along with it. Like the Mariner, Victor will live in isolation and fear. He seeks to tell his story to anyone who will listen, which turns out to be Walton. Walton is a mirror of the listeners of the Mariner's story in the poem. Thus Victor fulfills the comparison to the Mariner, haunted by his knowledge and his actions, tormented by his past.

The Ancient Mariner's trip was to the polar regions, just as Walton's trip. In fact, it was the"polar gods" who punished the mariner for killing the albatross. The reason they were so angry is that the mariner showed a total disrespect for nature. In his own way, Walton shows disrespect for nature by insisting his ship stay stuck in the polar ice because he is so obsessed with getting to the North Pole. When he finds Victor, he discovers that Victor is determined to tell his tale just as the mariner is forced to tell his tale over and over. Victor, however, knows he is dying, so he desperately wants Walton to remember his story and warn others of its consequences. This parallels the warnings of the mariner to the wedding guest. Fortunately, Walton does learn from Victor and the monster and eventually decides to row out of the ice.

To add to the answer already given, the poem shares another theme with the novel. The ancient mariner shoots an albatross, without thinking or considering what the possible consequences could be. This act was incredibly thoughtless and stupid, especially because albatrosses were supposed to be omens of good luck to sailors. Likewise, Victor does something incredibly stupid without considering what the possible consequences could be: he created a superhuman that is stronger, faster, and bigger than any human ever could be. Then he abandoned that creature, setting it free without education or connection, expecting that he could just go on with his life as usual and pretend that nothing out of the ordinary had occurred.

The mistakes committed by the mariner and Victor illustrate the importance of forethought; both do something without considering the possible consequences. Further, both harm innocents—the albatross was just a beautiful bird, and Victor's creature was born beneficent and good—and pay dearly for their transgressions.

One way in which this poem is important in Frankenstein is that it helps to set the tone and mood for the novel. It is set for the most part in the frozen northern seas, the kind of wild regions to which Walton, the intrepid explorer and frame narrator, is heading at the start of Frankenstein. Walton actually invokes the poem and its protagonist, the Ancient Mariner, in a letter to his sister and goes on to admit that

I have often attributed my attachment to, my passionate enthusiasm for, the dangerous mysteries of ocean to that production of the most imaginative of modern poets (letter II).

The poem, with its wild romantic setting and supernatural events, has inspired Walton to seek out the ends of the earth in a similar quest for adventure.

When narrating his own story, Victor Frankenstein also refers to ‘The Rime of the Ancient Mariner’, quoting a few ominous lines from the poem just after he sees the creature he made come to life for the first time, and which he has immediately come to regard as a ‘frightful fiend’ (Chapter 5) – a direct quote from the poem.

The poem, then, is invoked both by Walton and Frankenstein; and the figure of Frankenstein seems to exert a kind of fascination for Walton, just as the Ancient Mariner casts a spell on his listener, the Wedding Guest.

The poem is also very important in that it shares a major theme with the novel: the dangers of over-reaching, of trying to achieve too much. Frankenstein and Walton want to venture into places never before explored; Walton seeks to reach far-off places on the globe, while Frankenstein delves into the wildest realms of experimental science. Similarly the Ancient Mariner thinks he can challenge nature and shoots an albatross for no reason except that he can. But such audacity brings down great misfortune on his head as he loses all his crew and is forced to sail alone with the dead on terrifying seas. He has learnt his lesson by the end and seeks to pass it on to the awed Wedding Guest.

Frankenstein is also soundly punished for his presumption in creating the monster, and warns Walton against the dangers of unbridled ambition:

Unhappy man! Do you share my madness? Have you drank also of the intoxicating draught? Hear me, - let me reveal my tale, and you will dash the cup from your lips!’ (letter IV)

At the beginning of Frankenstein, Robert Walton writes to his sister, Margaret, from the frozen wastes of Archangel:

I am going to unexplored regions, to “the land of mist and snow,” but I shall kill no albatross; therefore do not be alarmed for my safety or if I should come back to you as worn and woeful as the “Ancient Mariner.” You will smile at my allusion, but I will disclose a secret. I have often attributed my attachment to, my passionate enthusiasm for, the dangerous mysteries of ocean to that production of the most imaginative of modern poets.

Here, Shelley uses the allusion to establish the imaginative, poetic streak in Walton’s questing nature. These lighthearted reflections on the eve of a great expedition contrast sharply with Victor Frankenstein’s quotation from the “Ancient Mariner” when he is living in fear of “the demoniacal corpse to which I had so miserably given life.” Victor walks the streets of Ingolstadt:

Like one who, on a lonely road,
Doth walk in fear and dread,
And, having once turned round, walks on,
And turns no more his head;
Because he knows a frightful fiend
Doth close behind him tread.

The quotations link Walton and Frankenstein in terms of their background and Romantic tastes in literature, but otherwise, the two men are separated and differentiated by the allusions. Walton specifically says that he will not be like the Ancient Mariner and “shall kill no albatross.” His quest, unlike Victor's, involves no blasphemy. Frankenstein, on the other hand, takes a simile from the poem and finds that it applies to him quite literally. Frankenstein is not like one who fears that a monster is following him. He is such a one. The words are more apposite for him than they are for the Ancient Mariner. Ironically, despite the Mariner’s fear, these words in the poem accompany the expiation of the curse and the lifting of the penance. In Frankenstein, however, they signal the very beginning of Victor’s harrowing flight from the abomination he has created. Walton responds to the romance of the voyage and the beauty of emerald-green ice in Coleridge’s poem. Frankenstein is fascinated by the terror and the curse.

What these two characters share is an obsessive compulsion to master nature, or to assert the primacy of the individual over time and space, in the case of the Mariner, or life and death, in the case of Frankenstein. Both men are haunted by their choices.

Mary Shelley knew Coleridge’s poem very well. Coleridge and her father, William Godwin, were friends, and there is a story of Mary, as a child, hiding under a sofa to secretly listen to Coleridge read “The Rime of the Ancient Mariner” to her father. In both texts the cost of the Mariner’s and Frankenstein’s respective quests is a kind of moral or mental hell. The quote is apt, not only because Shelley includes it in her novel, but because Victor is “embodying” the Mariner’s experience. The figurative fiend Coleridge mentions has become a real “fiend,” the reanimated corpse of the monster.

There is also a sense in which the monster and the albatross are connected. The albatross is a “good omen,” a sign from God which the Mariner kills, bringing on the death of his crewmates. On the other hand, the monster is a kind of inverse of the albatross—it is an “ill omen” that Frankenstein cannot kill. It’s also telling that the albatross’s status among the crew—it is a “fellow creature”—is precisely the status the monster desires for himself.

The characters are, on the surface, quite dissimilar, in that Victor Frankenstein is highly cultured, wealthy, and a brilliant scientist while the mariner is relatively uneducated, apparently working as an ordinary seaman. Victor's transgressions come from a form of intellectual arrogance in which he uses his vast intellectual gifts to fashion a monster, usurping the role of God. The mariner's transgression seems an act of impulsive stupidity and cruelty, not deliberately thought out at all. 

It is after these turning points, the death of the albatross and the monster's re-entry into Victor's life, that both characters engage in extended travels or quests to redeem themselves for their transgressions. Both stories include polar landscapes, the Arctic in Victor's case and the Antarctic in the mariner's, as scenes of ultimate desolation and danger. Both characters are compulsive storytellers, with their confessions serving as essential parts of their quests for redemption. For both characters, their punishments are both external ones and internal ones of mental agony that eventually bring them to realize the evil nature of their acts and attempt some form of reparation. 

Both were obsessed with their quests, Victor with creating life and the Ancient Mariner with his voyage. They become so blinded by their goals that they risk their own safety and others'.

The quote that you included is an excerpt from "The Rime of the Ancient Mariner" which  appears in Chapter 5 of Frankenstein right after Victor has brought the monster to life. The Mariner learned that there is no escaping the responsibilities or consequences of ones actions/choices.  Victor, on the other hand, looks behind him once and tries to put behind him the "fiend."

In the end, both fictional characters pay the ultimate price for their obsessions.

By alluding to this famous poem by Samuel Taylor Coleridge, Mary Shelley creates a mood of foreboding, but ultimately it is optimistic. Early on, Captain Walton writes to his sister, saying,

"I am going to unexplored regions, to 'the land of mist and snow;' but I shall kill no albatross, therefore do not be alarmed for my safety."

"The Rime of the Ancient Mariner" tells the story of an old sailor who, on a long voyage, killed an albatross and brought down a curse upon himself and the crew of his ship.  He tells the story of his misfortune to whomever needs to hear it and learn from it in order to avoid tragedy in their own life. Once Victor is introduced and he begins to tell his tragic story, one that he brought upon himself just as the mariner did, it begins to seem as though hearing Victor's story may prove efficacious for Walton if and when he must make a decision to avert potential tragedy.  This is what happens in the end, when Walton makes the difficult decision to return home at his crew's request rather than risk their lives for the sake of his own pride.  Although he sees this as a tragedy for him, Walton has clearly learned from both the mariner and Victor's stories, and this is a positive thing.

Both of these works are key entries in the Romantic literary movement. The Romantics emphasized the sublime, the supernatural, and madness in their creative output. Frankenstein was written and published relatively late in the Romantic movement, while "The Rime of the Ancient Mariner" was released right in the movement's heyday in the late eighteenth century, but the two share common aesthetic and technical affinities.

Frankenstein takes quite a bit from "The Rime of the Ancient Mariner," particularly its narrative framing structure. The Mariner in the present tells his story to those who will listen at the wedding, while Victor tells the events of Frankenstein as he is chasing the creature down in the North Pole.

Both works also revel in the sublime—a Romantic notion of the individual's feelings of being overwhelmed in the face of the greatness of the natural world. The Mariner, at first feeling superior to the sea and animals, comes to recognize the holiness of nature when he is alone on the ship, lost in the middle of a dangerous but immensely gorgeous ocean. The Creature feels awe at nature as well when he is wandering through the wilderness without a parental figure to guide him into the world.

Both works also share a sense of the supernatural. "The Rime of the Ancient Mariner" is packed with ghostly imagery, and the Mariner's experiences have a strong supernatural bent to them. Frankenstein is classically characterized as science fiction, but Victor's interest in alchemy and the mysterious circumstances under which he brings his creation to life evoke the idea of medieval sorcery. (Coincidentally, the Middle Ages were of great interest to the Romantics, who often idealized past eras.)

Mary Shelley herself, along with numerous critics, has acknowledged her debt to Samuel Taylor Coleridge's "The Rime of the Ancient Mariner" in her Frankenstein. Clearly, the epic of damnation and redemption influenced the impressionable teenage author of a novel with a similar theme. But another reason for the allusive presence of the poem in the novel can be summed up in one word: admonition. Both "The Rime of the Ancient Mariner" - told by the hapless seafarer to the captive audience of the Wedding Guest - and Frankenstein - ensconced in the letters of Robert Walton - are told from the second person point of view, the narrative of warning, prohibition and responsibility. Frankenstein's second person narrative, and the many allusions to "The Rime of the Ancient Mariner" is likely Mary Shelley's warning to the reader. But about what is the warning? The answer can be found in the direct reference to Coleridge's poem in the words of Robert Walton: he goes “to the land of mist and snow,” yet he swears that he shall “kill no albatross” nor, says he, shall he return “as worn and woeful as the ‘Ancient Mariner’”. His promise, like the grandiose quest of Victor Frankenstein, is ironic. Both men are carried away by a hubristic search for knowledge. It is only by listening to Frankenstein's cautionary tale about the cost of wresting the secret of life from God that Walton is dissuaded from playing God with the lives of his fellow-travelers. He turns back from his pursuit of personal glory, the fate of the ancient marier ringing in his ears. 

When answering this question, you should consider the themes of isolation and rejection in Frankenstein and “The Rime of the Ancient Mariner.” In Frankenstein, Walton, Victor, and the creature are all isolated. Walton is isolated on ship because he has no friends. “I have no friend, Margaret (Letter 2),” he tells his sister. Victor isolates himself when he chooses to study reanimation. “And the same feelings which made me neglect the scenes around me caused me also to forget those friends who were so many miles absent, and whom I had not seen for so long a time” (Chapter 4). The creature is similarly isolated when he is forced to roam alone in the mountains. When telling Victor his story, he concludes: “I am alone and miserable, man will not associate with me” (Chapter 16).

In “The Rime of the Ancient Mariner”, the Mariner tells a story of death and isolation to the Wedding Guest. After killing the albatross, the Mariner is left alone when all the other sailors die. “I looked upon the rotting sea, / And drew my eyes away; / I looked upon the rotting deck, / And there the dead men lay. / I looked to heaven, and tried to pray; / But or ever a prayer had gusht, / My heart as dry as dust.” The Mariner, who is at fault for the deaths of the men, must endure his guilt alone.

The theme of rejection also plays an important role in both the novel and the poem. In Frankenstein, the creature is rejected by his creator, by the cottagers, and by society as a whole. This rejection causes him to seek Victor relentlessly and ask him for a companion. He tells Victor: “I am malicious because I am miserable. Am I not shunned and hated by all mankind?” (Chapter 17). In “The Rime of the Ancient Mariner,” the Mariner first rejects the Albatross: “'God save thee, ancient Mariner! / From the fiends, that plague thee thus!-- / Why look'st thou so?'--With my cross-bow / I shot the ALBATROSS.” Later, the Mariner is rejected by the rest of the crew. “Ah ! well a-day ! what evil looks / Had I from old and young! / Instead of the cross, the Albatross / About my neck was hung.” The Mariner is rejected as a result of his actions. Rejection and isolation are related in both the book and the poem.

The Ancient Mariner of Coleridge's poem "The Rime of the Ancient Mariner" took a proud and arrogant view of nature when he killed the helpful albatross in the regions around Antarctica. He destroyed the bird for no reason, except that he could. For this deed, he was haunted and punished. To atone he must tell his story as a warning to other people to respect God and nature. The Mariner tells the wedding guest

He prayeth best, who loveth best
All things both great and small;
For the dear God who loveth us,
He made and loveth all.

Walton realizes that he too is a proud and ambitious explorer like the Mariner, and perhaps, like the Mariner, overstepping his bounds. Victor Frankenstein is also like the Mariner, driven by his ambition and disregard for God to go beyond his human limits and take life (in his case creating rather than destroying it) into his own hands.

Both the Mariner reference and Walton's own story suggest that Victor's ambition is commonplace, not an aberration.

This allusion to the Mariner is found in Walton's second letter to his sister, where he writes that he is fearful he will come home as "woeful" as the Mariner.

In Letter II of Frankenstein, Walton writes in the latter part of his missive to his sister that he is going to unexplored regions, to

'the land of mist and snow'; but I shall kill no albatross, therefore do not be alarmed for my safety, or if I should come back to you as warn and woeful as the 'Ancient Mariner'? 

Walton continues by telling his sister a "secret":  He has long had an enthusiasm for the "dangerous mysteries" of the ocean which has been influenced by his reading of Coleridge's poem.  And, as in Coleridge's poem, Walton's expedition is to the polar regions.  In fact, in "The Rime of the Ancient Mariner," the "polar gods" punish the sailor for his disrespect for nature by his killing of the albatross.  Similarly, Walton displays disregard for nature by later insisting that the ship remain stuck in the polar ice because he is so obsessed with reaching the North Pole.  Fortunately, of course, Walton is dissuaded by Victor Frankenstein and his crew, so he turns back from his mission. 

Both the Mariner and Frankenstein bring suffering to themselves and others through their own hubris or pride: they both start out thinking they can do whatever they want and only later learn to repent of their actions.

The Mariner's ship is saved from an ice jam near Antartica by an albatross, but the Mariner carelessly assumes the right to kill it, despite its kind act. As the Mariner says:

With my cross-bow,
I shot the albatross.

As a result of this killing, which shows contempt for God's creatures, the Mariner and his shipmates are cursed and led by spirits to a place where their ship is stranded by unmoving waters near the equator. The crew is parched with intense thirst;

Day after day, day after day,
We stuck, nor breath nor motion;
As idle as a painted ship
Upon a painted ocean.

Water, water, every where,
And all the boards did shrink;
Water, water, every where,
Nor any drop to drink.

Eventually, the crew members meet Death and die, while the Mariner is cursed to lead life in death.

Likewise, Frankenstein shows hubris or pride. He violates nature by acting like God and creating life out of dead body parts. He is an ambitious young scientist, and he is so bent on success that he doesn't think through the moral implications of what he is doing. When the creature comes to life, Frankenstein is horrified by its ugliness. Instead of taking responsibility for what he has created, he abandons his creation. Like the Mariner, who lacked empathy for the albatross, so Frankenstein lacks empathy as he deserts his creation. All Frankenstein can do is think about himself:

Now all was blasted: instead of that serenity of conscience, which allowed me to look back upon the past with self-satisfaction, and from thence to gather promise of new hopes, I was seized by remorse and the sense of guilt, which hurried me away to a hell of intense tortures, such as no language can describe.

Because of Frankenstein's rejection of the creature, including refusing to follow through on a promise to build a mate for him, Frankenstein's friends and family suffer the curse of being killed by the creature. This is similar to the crew dying because of the Mariner's deed. The monster kills Frankenstein's brother William, his close friend Clerval, and Frankenstein's fiancee. Frankenstein also suffers the fate of a sort of "life-in-death," becoming starved and sick as he chases the creature to the arctic, determined to destroy it.

Both the Mariner and Frankenstein think they can do whatever they want. They both learn, however, to regret and repent of their thoughtless actions regarding God's creation.

I am not sure where you are in Frankenstein, but both that novel and "The Rime of the Ancient Mariner" use a frame narrative. In other words, in both cases, the title characters tell their stories to a person they have never seen before. In the case of the Mariner, he relates his tale to a wedding guest. The guest is distressed that he can't get to the wedding festivities, but is nevertheless transfixed by the strange Mariner and compelled to listen to his story. In Frankenstein, Captain Robert Walton finds Victor Frankenstein half starved and floating on an ice floe in the Arctic. He too listens to a very strange saga, which he writes about in letters to his sister.

In both cases, too, the stories are about the suffering that is caused by each man—Victor and the Mariner—acting out of pride or arrogance. The Mariner violates the laws of God and man and brings down a curse when he arrogantly kills the albatross that saved his ship. Frankenstein, out of a sense of pride, violates God's law when he creates life out of inanimate body parts. He compounds the problem when he rejects his creation, who out of anguish at being unloved, kills the people closest to Victor. Both the Mariner and Victor live to regret what they have done.