As well as books and reading material online, nowadays you can also find video lectures...for example, the following was at the top of Googling "category theory video": http://golem.ph.utexas.edu/category/2007/09/the_catsters_on_youtube.html Cheers, Mike. Nick Rudnick wrote:
I haven't seen anybody mentioning «Joy of Cats» by Adámek, Herrlich & Strecker:
It is available online, and is very well-equipped with thorough explanations, examples, exercises & funny illustrations, I would say best of university lecture style: http://katmat.math.uni-bremen.de/acc/. (Actually, the name of the book is a joke on the set theorists' book «Joy of Set», which again is a joke on «Joy of Sex», which I once found in my parents' bookshelf... ;-))
Another alternative: Personally, I had difficulties with the somewhat arbitrary terminology, at times a hindrance to intuitive understanding - and found intuitive access by programming examples, and the book was «Computational Category Theory» by Rydeheart & Burstall, also now available online at http://www.cs.man.ac.uk/~david/categories/book/, done with the functional language ML. Later I translated parts of it to Haskell which was great fun, and the books content is more beginner level than any other book I've seen yet.
The is also a programming language project dedicated to category theory, «Charity», at the university of Calgary: http://pll.cpsc.ucalgary.ca/charity1/www/home.html.
Any volunteers in doing a RENAME REFACTORING of category theory together with me?? ;-))
Cheers,
Nick