Angelo the goldsmith and the Second Merchant are discussing how Antipholus of Ephesus claimed to have never received the gold chain from Angelo, when they encounter Antipholus of Syracuse and Dromio of Syracuse. Angelo sees the gold chain hanging from Antipholus' neck, and they exchange harsh words that lead to drawn swords. Just then Adriana, Luciana, and the Courtesan come in, and Antipholus and Dromio flee into a nearby abbey. The Abbess comes out and demands to know what is going on. Adriana describes her husband's madness, but after hearing the story, the Abbess blames Adriana's jealousy for driving Antipholus mad and denies everyone entry into her house, saying that she will cure the man herself.
It is now five o'clock, and Duke Solinus appears, leading Egeon to his execution. Adriana, seeing the Duke, appeals to him for aid in removing her husband from the abbey, describing his madness and their attempts to control him. The Duke, remembering promises that he made to Adriana when she married Antipholus, agrees to mediate--but just then a messenger comes in, with news that Antipholus and Dromio (of Ephesus) have escaped from Pinch's clutches. Adriana calls him a liar, saying that her husband is in the abbey, but then Antipholus himself rushes in, accompanied by his slave and demanding that the Duke grant him justice against his wife, who has locked him out of the house, allowed him to be arrested, and then placed him in the hands of Pinch. There is a flurry of charges and countercharges, and the Duke summons the Abbess, hoping that she can untangle the mess.
Egeon, meanwhile, goes up to Antipholus of Ephesus and, mistaking him for the son he brought up, and greets him happily. Antipholus E. is confused and says that he never saw his father in his life, and that he has always been a citizen of Ephesus. Then, mercifully, the Abbess enters, bringing with her Antipholus and Dromio of Syracuse, which causes general consternation. The Abbess greets Egeon and declares that she is his wife, Emilia, long separated from him, and that the identical Antipholi are their twin sons. The rest of the tangle is quickly explained: The ring is returned to the Courtesan, the gold chain is paid for, and the Duke refuses an offer of payment for Egeon's life, declaring that the old man is pardoned. Then, the entire company retires inside the Abbey for a celebratory feast, with the two Dromios going last, hand in hand, "like brother and brother (V.i.427)."
The final act consists of a mounting confusion that is finally ended by the intervention of the Abbess, Emilia. Her character appears for the first time here and acts as a kind of deus ex machina to untangle the web of errors in which the other characters are trapped. Her social status within the city, however, is a matter of debate: some critics see her as a priestess of Diana, the pagan protectress of Ephesus, while others see her as a Catholic nun. Making her a Catholic would be an interesting choice for a playwright surrounded by the fervent Protestantism of Elizabethan England; there are other references to Catholic practices in the text, especially from the two Dromios, who repeatedly refer to their "beads" (rosary beads) and cross themselves--both of which would have been immediately recognized as Catholic behavior by the religiously aware audience of Shakespeare's time.
Regardless of her religious affiliation, Emilia's appearance and explanation erases what was quickly turning into an ugly scene, as even the sensible Duke had begun to lean toward witchcraft as an explanation. "I think you have all drunk of Circe's cup (V.i.271)," he says, referring to a mythological Greek sorceress; and when the two pairs of twins are on stage together for the first time, he demands to know "of these, which is the natural man, and which the spirit? Who deciphers them?"(V.i.335-6). The decipherer, of course, is Emilia, and her quick explanation is such a relief that the audience may gloss over the peculiar question of why she spent 20 years in Ephesus without ever revealing herself to the son who was living there, let alone telling him about the missing half of his family. This is a farce, so we accept a little improbability--after all, the fact that both Antipholus brothers (along with their servants) are wearing the same clothes on the day that they meet in Ephesus is coincidence enough to make all others pale in comparison.
So all ends happily, and even the Duke, previously a model of legalism, is willing to waive the requirements of his city's law in the face of such general happiness. It is worth noting, however, that the Antipholus brothers seem less than enthusiastic to finally meet one another. The Ephesian twin is anxious to get back to his wife and his role as a solid citizen and tradesman, while the Syracusan seems to have overcome his earlier angst and spiritual incompleteness and wants to get down to the important business of pursuing Luciana. Significantly, it is their slaves, the comic centers of a comic play, who are most affected by the reunion. "I see by you I am a sweet-faced youth (V.i.421)," Dromio of Ephesus says, and then they walk offstage arm in arm, as two happy clowns should.
I have written my own act wise summary of comedy of errors. Hope it will help students like me.