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 Gödel's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises.

'As well as having a better understanding of Category Theory, I have a new perspective on theoretical computer science: the subset of functions that comprise computable functions is somewhat ugly to formalise. This is the first in a series of Cambridge Elements: shortish works on Applied Category Theory. This one is highly recommended: I will be looking out for the others.' Susan Stepney, (http://susan-stepney.blogspot.com)