What are the two major allusions in the book Frankenstein?
From your spelling, you are asking about references to famous works, people, places, etc., not "illusions". The whole title of the novel is Frankenstein, or the Modern Prometheus. This is an allusion to the Greek god Prometheus who created mankind and then gave his creation fire, giving them an advantage over other animals. This angered Zeus, and he punished Prometheus by chaining him and having an eagle eat his liver day after day. Dr. Frankenstein doesn't love his creation as Prometheus did, but Frankenstein must suffer eternally for overstepping the boundaries of science.
Another allusion is to the creation of Adam and Eve. The monster appeals to Frankenstein by saying he should be Frankenstein's Adam, a Biblical allusion. The monster says he is instead a "fallen angel". The monster brings up Eve to show how lonely he is, that God in his mercy created a mate for Adam and, if Frankenstein is going to act like God, he should give the monster a mate as well.
Another major allusion is to Samuel Coleridge's epic poem, "The Rime of the Ancient Mariner". 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." One particular excerpt from the poem parallels Victor's mood and actions.
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.
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.
Of course, you ask about allusion, with an "a", rather than illusion, with an "i", so I'll deal with the first major allusion in Shelley's Frankenstein, or the Modern Prometheus. It's in the title.
In ancient Greek myth, Prometheus creates men out of clay. That, of course, is what Frankenstein does in the novel, although he does not use clay, exactly, and his is a creation based on science. The story is told by Walton, as told to him by Frankenstein.
Specifically, the story of Frankenstein creating life in the form of what he comes to see as a monster, begins in chapter IV of Frankenstein's narrative via Walton. Frankenstein loses his health and suffers greatly while creating the monster, but, of course, his worst suffering is yet to come.
I am not sure if you mean literary illusions or objective illusions. If I were to look at the illusions that I observed in the book Frankenstein it is that Victor Frankenstein appears as good and turns out to be bad and the creature appears to be bad and turns out to be the victim.
Victor Frankenstein is introduced to us as an ill man who is in repentance for something from the past. He tells his story to Watson, the ship's captain, who likes him and establishes a friendship with Victor.
Victor appears to be a nice and ambitious young man and a loving son. He had a good and adventurous childhood, loves his parents, his younger brother and Elizabeth, his cousin and future wife. He is also very intellectual and attends the University where he struggles to learn new medical methods and everything that he can to create a being that would be resistive to disease. This is the result of his trauma over his mother's death.
However, the more the reader learns about Victor, the more the illusion fades. The reader begins to see a selfish young man who is driven by ambition on the idea of the glory of playing "God" by creating man. He goes to deep unethical depths to collect body parts and puts them together to create a human being. He does not think about the human's reaction to being created nor the outcome of what the being would look like based on the scraps of bodies that he has pieced together.
Once the creature comes to life, Victor is appalled by his creation and abandons him. The creation is left desperate and alone in a world that finds it repulsive and grotesque and fearful. In the end Victor has the benefit to escape the creature by his own death.
The illusion of the creature is hat he has the physical appearance of a monster when he is actually a being desperate for love, touch, and companionship. Every time he approaches a human they run, scream, and try and hurt him. Even his own "father" rejects him and tries to do away with him.