Our hero, Lemuel Gulliver, really likes being at sea. He likes observing people. So, he doesn't seem too sad about the fact that he has to leave his wife and become a sailor again after a brief hiatus of domestic life in England. We have chosen to focus on Gulliver's slow turn against mankind as the main plot line of Gulliver's Travels; Gulliver's initial situation is one of relative open-mindedness about people, as he uses his time to learn languages and read books.
In the first chapter of his adventures, Gulliver washes ashore on Lilliput, an island filled with tiny people whose size and relatively foolishness (e.g., egg cracking is, like, a religion there) make him feel pretty secure. Oh sure, he's still at the whims of court intrigue and politics, but he is rarely in real danger of anything, since he could easily kill a Lilliputian with his foot if he needed to. At the same time, Lilliput is Gulliver's first experience (in this novel at least) of the pettiness of human affairs – the first sign of his growing discomfort with people.
So, the Lilliputians introduce the whole idea of poor government and hypocrisy. The Brobdingnagians really bring this home to Gulliver, and literally: as the small person in this scenario, Gulliver is at the mercy of the Brobdingnagians. So when the King criticizes Gulliver's home country, England, there is nothing Gulliver can do but sit there and take it. Gulliver's ego takes a bit of a blow, too: he is nearly killed by a frog, a cat, and a young puppy. He's no longer exactly the Superman he was in Lilliput.
In Part 2, Chapter 7, Gulliver offers to show the Brobdingnagian King how to make gunpowder. When the King refuses in horror, Gulliver uses this denial as proof of how naïve and ignorant the Brobdingnagian King really is. At the same time, at the conclusion of the novel, Gulliver acknowledges that the least evil among Yahoos are the Brobdingnagians, "whose wise maxims in morality and government it would be our happiness to observe" (4.12.4). In other words, he has come to see that the Brobdingnagians are, indeed, superior to the European Yahoos and the Lilliputians. This act of refusal of gunpowder provides an example for Gulliver of an alternative approach to governance that he cannot take on board yet – but he will eventually.
The third part of Gulliver's Travels is essentially what happens as we are waiting for Gulliver to acknowledge the defects of humankind that he keeps observing. While the other three parts really focus on governance and morality, the Laputian saga satirizes science. Oh, there's some stuff about mismanagement of lands in there, but it represents something of a digression from the main plot of the novel.
The denouement is the part of the book where everything becomes clear. When Gulliver first meets the Yahoos and is completely disgusted, he sees, for the first time, humans as we really are, without any of the disguises that clothing and good grooming might offer. On the other hand, the kindliness and rationality of the Houyhnhnms provides a foil for everything that humans aren't. The entire novel has been working up to this revelation: it's not England versus France or Europe versus the world – all humans are, at heart, awful.
Following Gulliver's revelation that people are gross and terrible, he decides to stay with the Houyhnhnms forever. When they won't allow him to stay, he tries to find a deserted island. When he finds a Portuguese ship arriving at his island, he attempts to avoid it and then to jump overboard. When he arrives in England, Gulliver cannot be in the same room with his wife and children because of the way they smell. Gulliver's transformation is complete: he's gone from a pretty friendly guy to a complete, total man-hater.