Category Theory introduction? yeah, sure...

MacLane

Eilenberg

There is plenty of material on category theory around. Collecting here some old favorites and some newer stuff that I haven't checked out,  yet.

The familiar:

S. Mac Lane, Categories for the Working Mathematician (1971, 1998)

R. Goldblatt, Topoi, Dover reprint and online (1979, 1984, 1986, 2002).

J.-Y. Girard, Y. Lafont, P. Taylor, Proofs and Types (1989) online 

V. de Paiva, Categorical Proof Theory and Linear Logic, ESSLLI, Prague (1996) google doc sideways(!) available

D. Crouch, J. Genabith, Linear Logic for Linguists, ESSLLI (2000), notes

J. Gallier, Constructive Logics. Part I: A Tutorial on Proof Systems and Typed lambda-Calculi, paper

Then some traditional fare:

R. Blute P. Scott, Category Theory for Linear Logicians (2003)

F.W. Lawvere, S.H. Schanuel, Conceptual Mathematics (1997)

S. Awodey, Category Theory, (2010)

H. Simmons, An Introduction to Category Theory, CUP, (2011) online version

Adámek, Jiří, Herrlich, Horst, & Strecker, George E.; (1990). Abstract and Concrete Categories Originally publ. John Wiley & Sons. ISBN 0-471-60922-6. (now free on-line edition). 

M. Barr, C. Wells, Toposes, Triples and Theories, 1983, now online.

Then more adventurous (perhaps??) stuff:

M. Stay, Category Theory in JavaScript.

M. Johansson, Category Theory and Functional Programming, Stanford FALL 2009 course and St. Andrews 2012 notes   (99 pages)

also Chalmers discussion group

Abramsky and Tzevelekos, "Introduction to Categories and Categorical Logic" (2010)

G. Hutton, Introduction to Category Theory, Midlands Graduate School notes, 2012.

D. Verity, An Introduction to Category Theory - FP-Syd talk.

E. Cheng, The Catstars, YouTube channel.

J. van Oosten, Basic Category Theory, 2002, notes

L. Maertens, Category Theory for Program Construction. ESSLLI notes (1995)

S. Easterbrook, An introduction to Category Theory for Software Engineers, slides

Further afield:

• Sets for Mathematics by F. W. Lawvere & R. Rosebrugh.
• Topoi: The Categorical Analysis of Logic by R. Goldblatt.
• Abstract and Concrete Categories: The Joy of Cats by J. Adamek, H. Herrlich, G. Strecker.
• Categorical Logic by A. M. Pitts. 
• Stone Spaces by P. T. Johnstone.
• Sheaves in Geometry and Logic: A First Intorduction to Topos Theory by S. Mac Lane & I. Moerdijk.
• Handbook of Categorical Algebra (three volumes) by F. Borceux.