Using basic category theory （category， functor， natural transformation， etc。）， this Element describes all the central concepts and proves the main theorems of theoretical computer science。 Category theory， which works with functions， processes， and structures， is uniquely qualified to present the fundamental results of theoretical computer science。

In this text， we meet some of the deepest ideas and theorems of modern computers and mathematics， e。g。， Turing machines， unsolvable problems， the P=NP question， Kurt Gödel’s incompleteness theorem， intractable problems， Turing’s Halting problem， and much more。 The concepts come alive with many examples and exercises。 This short text covers the usual material taught in a year-long course。