  This is a short introduction to categories with some emphasis on coalgebras.
We start from introducing basic notions (categories, functors, natural
transformations), move to Kleisli tripels and monads, with a short discussion
of monads in Haskell, and continue with displaying the interplay between
algebras, adjunctions and monads. Coalgebras are discussed and applied to the
semantics of modal logics, giving a brief introduction to coalgebraic logics as
well. The development is illustrated through examples, usually taken from
applications to computer science, with a certain predilection for stochastic
systems.
