Using basic category theory, 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 Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Goedel’s incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing’s Halting problem, and much more. The concepts come alive with many examples and exercises.