Toposes, Triples and Theories by Michael Barr and Charles Wells.
From the preface:
Chapter 1 is an introduction to category theory which develops the basic constructions in categories needed for the rest of the book. All the category theory the reader needs to understand the book is in it, but the reader should be warned that if he has had no prior exposure to categorical reasoning the book might be tough going. More discursive treatments of category theory in general may be found in Borceux [1994], Mac Lane [1998], and Barr and Wells [1999]; the last-mentioned could be suitably called a prequel to this book.
So you won’t have to dig the references out of the bibliography:
M. Barr and C. Wells, Category Theory for Computing Science, 3rd Edition. Les Publications CRM (1999).
Online at: http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf
F. Borceux, Handbook of Categorical Algebra I, II and III. Cambridge University Press (1994).
Cambridge Online Books has these volumes but that requires an institutional subscription.
S. Mac Lane, Categories for the Working Mathematician 2nd Edition. Springer-Verlag, 1998.
Online at: http://www.maths.ed.ac.uk/~aar/papers/maclanecat.pdf
Enjoy!