Before he chose to diddle away his later years writing book after book of history, playing house with Rousseau, annoying the religious authorities, and forging a lasting reputation as an all-around good guy, Hume dedicated his youth to writing the this book, which is nothing less than the single greatest work of philosophy in the English language. Indeed, I don't think there are even any other close competitors for that title. Naturally, then, this work was largely ignored during Hume's lifetime.
Notwithstanding the widely told, and somewhat accurate, standard story of the history of modern philosophy according to which Kant's rearguard action in response to Hume is the culmination of the modern period, I think that this book rather than Kant's First Critique is where it's at. Certainly, no book of modern philosophy compares to this complex, intricately argued, inspiring, maddening, imaginative, iconoclastic, encyclopedic tome when it comes to influence on contemporary philosophers in the Anglo-American analytic tradition. And while it's true that Kant's system is almost unparalleled in the breadth of its influence, defenders of the traditional story of modern philosophy need to remember that 'almost'. For it seems to me that, among the moderns, Hume got there first. He, and not Kant, is the first modernist whose importance is manifest in all the main areas of philosophy: epistemology (skepticism and the problem of induction), metaphysics (causation, personal identity, etc.), philosophy of mind (action theory, rationality) meta-ethics (meta-ethical subjectivism, proto-noncognitivism, reason vs. emotions, moral psychology, etc.), normative ethics (importance of benevolence, justice as an artificial virtue, etc.).
Want some evidence of Hume's pervasive influence? It's not just that everyone working in this tradition has read Hume, though they have. Nor is it just that Hume's stamp is all over the concerns and positions of contemporary philosophers, though it is. Nor is it just that Hume's influence is celebrated (or bemoaned) by pretty much every philosopher you come across, though that's true as well. No, the true measure of his intellectual ascendancy is that there's a position dubbed "Humean" in pretty much every area of philosophy, and, depending on one's view of the topic, it's either the obviously correct view--it was Hume's position, after all!--or a pernicious heresy for which no good arguments have been provided and for which there isn't good reason to think it was even Hume's actual position. You know you've made it when both the defenders of the status quo and those who can't abide that status quo claim you as their own.
Why is Hume so important? I think there are two reasons, each corresponding to one of the influential interpretations of Hume's work as a whole. The first interpretation of Hume's corpus sees it as shot through with a radical skepticism about anything and everything, and corresponding to this interpretation is a conception of Hume's importance as consisting in his occupying the place of the philosopher opponent of common sense par excellence. Hume, according to this interpretation, takes the empiricism of Locke, which in his hands looks like nothing so much as self-conscious common sense, and wields it as a weapon against more or less everything we tend to believe. That is, we should see Hume as taking up the empiricism of Locke and Berkeley and pushes it to its logical conclusion: a thoroughgoing skepticism. Think you can know there is a mind-independent world of physical objects? Think you're a single person who persists through time? Think things stand in causal relationships to one another? Think you can know whether the sun will explode tomorrow? You should think again, Hume says, and he's happy to show you why empiricism leads to this conclusion. So, if this is right, the importance of Hume's project consists in its status as a for rationalists, for non-skeptics of all stripes, and for all ordinary, right-thinking folks.
Now, undoubtedly, there's some truth in the stereotypical view of Hume as the young radical who took empiricism to its implausible limits. But this isn't where his true importance lies--at least not among contemporary philosophers. What has been most influential among contemporary exponents of the Anglo-American analytic tradition is Hume's unrepentant and radical naturalism. This interpretation of his project downplays Hume's skepticism and emphasizes his professed intentions to provide a positive account of the operation of the human mind that appealed to nothing beyond the evidence of our senses. According to proponents of this interpretation, Hume is most interested in a description of the operation of the human mind. He's describing what human nature allows us to know and what it doesn't allow us to know. Here Hume's importance consists not in his providing a challenge to the views of philosophers and of the hoi polloi, but in his providing us with a model of how philosophy should be done.
I feel that I've strayed somewhat from the topic of the book here, but I suppose that was inevitable. It would, of course, have been pointless to attempt to summarize Hume's arguments, or even his conclusions, in a review of this length. The only summary of this book's content that the reader needs is this: Hume discusses nearly everything of importance in philosophy, and his discussions of nearly every issue reveal an unsurpassed (and rarely equaled) level of philosophical brilliance.
To whom do I recommend this book? The answer, in short, is everyone. If you're even slightly interested in philosophy, you simply can't get by without reading this. If you're at all interested in the history of ideas, you need to read this. If you're the slightest bit curious about our modern worldview and its origin, it would be a good idea for you to read this. If you're interested enough in Hume to have come across this review and read it to this point, you'll want to read this.
Concerning editions of this book. I wish Amazon would separate the various editions of this book so I could review them separately, but they haven't. I'd recommend either the edition jointly edited by the Nortons and published in the Oxford Philosophical Texts series or the Selby-Bigge edition, which was for some time the standard edition of the Treatise.