If you want an actual introduction to the topic, "Conceptual Mathematics: A First Introduction to Categories" by Lawvere and Schanuel is the right choice.
Funny coincidence, I just found this video http://www.reddit.com/r/haskell/comments/1l4ph3/dsls_and_tow... back, where the speaker mentions many CT ideas (adjoint functors, galois connections) and end up pointing at abstract interpretation and Lawvere work.
Seconded. To elaborate, it is essentially a lightly edited transcription of all the lectures of an undergraduate introduction to categories course, complete with diagrams, exercises, and dialogue, and even including students' answers (right and wrong!) to review questions. It's a very unintimidating format, and the book does very well to help a beginner get firm footing with the foundations.
Sure, it's concise, but I'd hardly describe ncatlab as introduction. It's more of a reference. I'd dare say the Wikipedia entry on category theory (and related links) makes a better introduction for the uninitiated.
To actually learn it, Mac Lane & Saunders "Categories for the Working Mathematician." seems to enjoy continued popularity.
MacLane is still the standard for working mathematicians, but for those with less background, Steve Awodey's book[1] is very good. He also has some YouTube lectures[2]. While you're on YouTube, the Catsters channel[3] has many excellent 10-minute category theory videos.
I can second the Catsters channel. As a complete category theory newbie watching those videos was nevertheless enjoyable because of the upbeat and cheerful attitude with which the material was covered.
I actually found MacLane's book to be more approachable than Awodey's. Although I'm not sure this is good advice because it took me several years casually feeling my way through the field to start to gain an understanding into it (ie YMMV).
Interesting category theory historical fact! Checkout MacLane's wikipedia page and you will find one of his students was in fact Steve Awodey.
> To actually learn it, Mac Lane & Saunders "Categories for the Working Mathematician." seems to enjoy continued popularity.
This is the best way I've found so far, and I had been semi-supplementing with MacLane and Birkhoff's "Algebra", just to get a feeling for the vocabulary; bringing myself from the space I typically mathematically exist in, to the space of category theory. Nothing else really has come close in composing the correct thought direction. It is dense, but I enjoy it very much. It is very beautiful math.
I have always sworn by Borceux' Handbook of Categorical Algebra. It progresses smoothly all the way from first principles up to (if you buy all three volumes) sheaves and topoi, but it is kind of expensive.
