I wrote a first course in category theory which I think more or less contains what's presumed knowledge in not too specialized papers and thesises (in computer science). It's 75 pages. The synopsis is: 1. Categories and functors. Definitions and examples. Duality principle. 2. Natural transformations. Exponents in Cat. Yoneda lemma. Equivalence of categories; Set^{op} equivalent to Complete Atomic Boolean Algebras. 3. Limits and Colimits. Functors preserving (reflecting) them. (Finitely) complete categories. Limits by products and equalizers. 4. A little piece of categorical logic. Regular categories, regular epi-mono factorization, subobjects. Interpretation of coherent logic in regular categories. Expressing categorical facts in the logic. Example of \Omega -valued sets for a frame \Omega. 5. Adjunctions. Examples. (Co)limits as adjoints. Adjoints preserve (co)limits. Adjoint functor theorem. 6. Monads and Algebras. Examples. Eilenberg Moore and Kleisli as terminal and initial adjunctions inducing a monad. Groups monadic over Set. Lift and Powerset monads and their algebras. Forgetful functor from T-Alg creates limits. 7. Cartesian closed categories and the \lambda-calculus. Examples of ccc's. Parameter theorem. Typed \lambda calculus and its interpretation in ccc's. Ccc's with natural numbers object: all primitive recursive functions are representable The notes are available by anonymous ftp via: ftp ftp.daimi.aau.dk cd pub/BRICS/LS/95/1 get BRICS-LS-95-1.ps.gz Jaap van Oosten