What are the important topics and questions in Gulliver's Travels?
The text raises some important questions about human nature and our flaws. Certainly, Swift satirizes our violent tendencies and lack of tolerance for differences among ourselves. When Gulliver describes the Lilliputians and their conflict regarding which side of the egg to crack, the bigger end or the smaller one, Swift points out the uselessness of the disagreements over religion in his own world. Many thousands of Lilliputians have died as a result of this ridiculous disagreement, just as many thousands of people English were killed as a result of the conflict between Protestants and Catholics. Swift implies that fighting over which religion is best is like fighting over which end of the egg to crack: it doesn't matter what your neighbor does or what you do. Each can practice whichever faith they desire and all should be able to get along.
In the land of the Houyhnhnms, the Yahoos satirize greed and ruthlessness. His Houyhnhnm master tells Gulliver that, even if there is plenty of food to go around, each Yahoo will try to hoard as much as he or she can, even if it means that others go without. They even kill each other over shiny stones and the like, simply because they want to have them.
Swift uses satire to encourage the reader to think critically about many of the things humanity does: the way people exploit each other for personal gain, the way people deny each other basic necessities so that we can have more, the way people kill each other over disagreements in ways of life that have no real effect on their own, and so forth. These are some of the most important topics Swift raises in the text.
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It helps the reader of Gulliver's Travels to know the various types of government that existed in the world of Swift's time; and some of the philosophical discussions for changes to existing governments or proposals for new types of government, I think, as I recall.