B.C. Pierce (1991) Basic Category Theory for Computer Scientists MIT Press. ISBN 0-262-66071-7. (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. ISBN 0-521-47817-0 (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. ISBN 0-19-856861-4 (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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