What is the relationship between the four plot lines (Athenian lovers, fairies, royalty, rude mechanicals) of A midsummer Night's Dream?
In Shakespeare's A Midsummer Night's Dream, comedy finds its way into all four plot lines, though less with nobility, and more with the lovers, fairies and common-workers-turned-actors.
It may be that the noblemen, especially the Duke, Theseus, represents that reality of the world: it is in this world that we learn Helena must marry someone she does not love. If she refuses her father, based on Athenian law, she could be put to death at her father's request.
However, once the young people (and the "actors") enter the fairy realm of the forest after dark, the rule of a parent or a Duke count for nothing. The world is transformed into a magic place of magic and nature and love: lots of it, and several different kinds—love embraced, love rejected, and love brought on by magic.
In terms of the relationship, what seems to move the plot at the beginning are the Duke's preparations for his marriage to Hippolyta (the Queen of the Amazons). He has won her in battle but hopes to woo her in matrimony.
The other plot exists between Helena and Lysander who love each other. Their love has been rejected by Hermia's father.
The fabric of the story weaves these two plot lines with the affairs of the fairy realm, where Oberon, the King of the Fairies and his Queen Titania are in the midst of a "lovers' quarrel," and the players enter the woods to practice their play in hopes that it will be selected as the entertainment for the Duke's impending nuptials.
The play, in some ways, seems at times like a Chinese fire drill because so much is going on. The Duke's wedding is tied directly to the players. The players get caught up in the fairy's entertainment. The fairies are there to bless the Duke's wedding, and the Athenian lovers are supposed to be directed by the hand of the Duke in affairs of the heart, but end up where they wish to be, married at the play's conclusion with the Duke and Hippolyta.
By the play's end, the four plot lines have been untangled, and life returns to "normal" for both the humans and the fairies. The crossover between the two worlds seems to be merely a dream to the Athenian lovers, and Puck apologizes to the "human" audience, hoping no one has been offended by the pranks the fairies have played on the humans.
I cannot say for certain why Shakespeare brings all these groups together except that, for one, his audience would have been made up of the kinds of people in the play (except for the fairies...). The poorest and the wealthiest would have seats in the same theater: the nobility would be seated in the "nose bleed section," and the peasants would have had front row seats. There was something for everyone in this comedy.
Love is a common theme in the play and this would be something the entire audience would appreciate. The presence of the fairies would also have been entertaining to the theater goers. Perhaps most of all, love and laughter would have been perfectly paired.
Whereas Shakespeare once wrote, in The Tempest, "Misery acquaints a man with strange bedfellows," in this case it would appear that love has done the same in A Midsummer Night's Dream.