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Lawvere & Schanuel. (1997). Conceptual Mathematics: A First Introduction to Categories Cambridge University Press. ISBN0521010608
B.C. Pierce (1991) Basic Category Theory for Computer Scientists MIT Press. ISBN0262660717. (Short and concise introduction. Probably not enough exercises for most people to really learn it from.)
And requiring somewhat more:
Lawvere & Rosebrugh. (2003). Sets for Mathematics Cambridge University Press. ISBN0521478170 (set theory axiomatized through category theory, for advanced undergraduates and beginning graduates; more advanced and then Lawvere & Schanuel. Starts fairly easy but seems to get harder.)
Awodey, Steven (2006) Category Theory (Oxford Logic Guides 49) Oxford University Press. ISBN0198568614 (very elegant, from what AA has seen of the no-longer-available downloadable pdf version, but perhaps a bit demanding for teacherless beginners with modest talent).
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