I've been planning to read some of Kant's work for a while, but have no idea where to start. Which of his writings would be a good initial introduction to his philosophical views?
I would start with Prolegomena to Any Future Metaphysics and then Groundwork of the Metaphysic of Morals for a broad introduction to many of Kant's most famous ideas. If you want to take a step further into the ideas introduced in those books, continue with the Critique of Pure Reason and the Critique of Practical Reason, respectively.
Note: There's nothing wrong with reading the books in any order intrinsically, but the Critique of Pure Reason is quite dense such that even the greatest minds will have difficulty parsing the text without a little guidance, if only because the translation between "old-timey" German and modern English leaves a little to be desired. I would definitely wait to read that until after already having digested some Kant, or under the guidance of a professor who specializes in Kant.
I don't think there is. Let me unwrap that a bit: First, there is not one book by Kant himself that touches upon all the topics he wrote about. He was very very strict about keeping different matters apart, so every book has its own matter, and one of them can't serve as an introduction to other ones, at least not consistently, and that's second: Kant didn't know everything he wrote down when he started - many of his pre-critical writings were later dismissed, and the practical writings often disagree in certain aspects.
The Critique of Pure Reason was meant to be an "introduction" - Kant wanted to write the Metaphysics of Morals but noticed that he had to do all the groundwork first. But starting with the Critique seems to be a bad idea. If you really want an introduction into Kant, as a whole system, I would absolutely recommend reading secondary literature. If not, start with the Prolegomena and the Groundwork of the Metaphysics of Morals.
Although I generally dislike Dover’s editions, I do like their edition of Kant’s “Logic”; which is—I think?—something derived from his students’ notes on his logic lectures? It covers the synthetic-analytic distinction well and in general the schematic contour of Kant’s work in other more formidable works like the three critiques. And once you are ready for the Really Big Stuff™, personally, I found the Kritik der Urteilskraft (n.b. the English word “judgment” lacks the teleological overtones of urteilskraft) much more inspiring than Kant’s other works (which I like, but am not strictly floored by). The remarkable arc of Kant’s thought from art and aesthetic judgment—pure ballistic—straight down to the ultimate purpose of the Universe is one of the most beautiful topical trajectories in all of philosophy…
But with Kant my best advice is to keep reading and don’t give up, and don’t get too swayed by secondary literature on Kant—of which there is a near-infinite supply.
I took an introductory moral philosophy class at Stanford a few years ago, and had the distinct privilege of being introduced to Kant by way of Groundwork of the Metaphysics of Morals, Harvard scholar Christine Korsgaard's thoughtful critique thereof, and Michael Sandel's accessible commentary in Justice. I would enthusiastically recommend immersing yourself in a combination of these texts for an introduction to Kant and to his immensely powerful "Categorical Objective."
+1 for a Prolegomena to Any Future Metaphysics. Someone suggested I read A Prolegomena to Any Future Metaphysics first, I did and it was a brilliant introduction. I would then suggest you read the Critiques starting with A Critique of Pure Reason.