  This is a draft of the textbook/monograph that presents computability theory
using string diagrams. The introductory chapters have been taught as graduate
and undergraduate courses and evolved through 8 years of lecture notes. The
later chapters contain new ideas and results about categorical computability
and some first steps into computable category theory. The underlying
categorical view of computation is based on monoidal categories with program
evaluators, called *monoidal computers*. This categorical structure can be
viewed as a single-instruction diagrammatic programming language called Run,
whose only instruction is called RUN. This version: improved text, moved the
final chapter to the next volume. (The final version will continue lots of
exercises and workouts, but already this version has severely degraded graphics
to meet the size bounds.)
