This play not only has a love triangle, it expands its geography to almost every character in the story.
Hermia is desired by Demetrius, who we can all identify as the arrogant bloke who is also having intimate times with Helena, who in turn is in love with Demetrius. Who Hermia truly desires is Lysander, not in approval her father Egeus. Theseus is brought in to point out that if Hermia does not give into Demetrius, she could either die or live the rest of her existence worshipping Diana, with chastity intact.
In Shakespeare's society, the father was the sole decider and deviating from the decision was thought to lead in disaster. Women were thought to make any real progress in society if they married, set by masculine standards. Eegeus' righteousness causes Hermia and Lysander decide to rebel anyway, wandering into the woods.
This form of Theseus is familiar for those who have read Geoffery Chaucer's "The Knight's Tale." He was a man of strong arm, strong will and utmost authority who tried to use it on everyone in his eyesight, including two lovestruck Theban knights Arcite and Palamoun. Here, Theseus is not in control of the situations in "A Midsummer Night's Dream" serving as the adult figure who cannot take reigns on youth itself.
So who decides the madness running amuck in this comedy? Meet Puck, also known as Robin Goodfellow, is set to create chaos with orders given by Oberon, King of the Fairies. He is known throughout folklore as a trickster, sometimes as a devil. More information on Puck can be found here.
In the course of events, Puck accidently sets Lysander's affections towards Helena, hurting Hermia's mood tremendously. Of course, Demetrius, who was never loving in mind with Helena to begin with, starts to rival with Lysander thanks to Puck's magic.
The love, or at least the confusion of love, does not stop there. Nick Bottom, a weaver among the "rude mechanicals" who are trying to orchestrate a play about Pyramus and Thisby, gets stuck with the head of an ass, even though he declared never to be made an ass himself! It is quite funny how Shakespeare plays with expressions, with Bottom being an example of how an expression can take a life of its own.
Titania, thanks to Puck's substance, falls for the ass-headed Bottom. Poor Bottom only becomes a tool for Titania to give up an Indian boy to Oberon. Once Puck lifts the spell, Bottom's fun comes to an end. Titania survives the encounter with absolute disgust. Sometimes love doesn't go in so well.