Hume was born in Edinburgh and attended the university there. At first he considered a career in law, but came to have, in his words, "an insurmountable aversion to everthing but the pursuits of philosophy and general learning."
He did some self-study in France, where he also completed A Treatise of Human Nature at the age of 26. When published in England (1739-40) it received next to no attention. Hume famously wrote that it "fell dead-born from the press."
After a few years of service to various political and military figures, Hume returned to his studies. After deciding that the problem with the Treatise was style not content, he reworked some of the material for more popular consumption in An Enquiry Concerning Human Understanding. It was not extremely successful either, but more so than the Treatise.
He was turned down for chairs of philosophy in Edinburgh and Glasgow, probably due to charges of atheism.
However, between philosophical pursuits, Hume did achieve literary fame as an essayist and historian. Attention to his works grew after Immanuel Kant credited Hume with awakening him from "dogmatic slumber".
Book 1: "Of the Understanding" His treatment of everything from the origin of our ideas to how they are to be divided. Important statements of Skepticism.
Book 2: "Of the Passions" Treatment of emotions.
Book 3: "Of Morals" Moral ideas, justice, obligations, benevolence.
He intended to complete the Treatise (if it met with success) with books devoted to Politics and Criticism.
Contains reworking of the main points of Treatise, Book 1, with the addition of material on free will, miracles, and the argument from design.
Another reworking of material from the Treatise for more popular appeal.
Discussions between fictional characters Cleanthes, Philo, and Demea. They discuss proofs of the existence of God and other fun stuff.
A lot of Essays, revised a few times during his life. The history of which essays were added or removed when doen't seem that interesting. "Of the Middle Station of Life," "That Politics may be Reduced to a Science," "Of the Origin of Government," "Of Civil Liberty," "Of Commerse," "Of the Populousness of Ancient Nations," and "On Suicide" (posthumous) to name a few in a modern collection.
More a category of books than a single work.