This is a draft of the first 8 chapters of a 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: changed the title, worked on improving the text. (Also added lots of exercises and workouts, but that was overflowing the arxiv size bounds already in the earlier version, which is why the "workouts" and the "stories" are commented out.)

翻译：本文是教材/专著前8章的草稿，基于弦图理论呈现可计算性。导论章节已在研究生和本科课程中讲授，并经过8年讲义迭代而成。后续章节包含关于范畴可计算性的新思想与成果，以及迈向可计算范畴论的初步探索。其底层范畴计算方法基于带有程序评估器的幺半范畴（称为*幺半计算机*）。该范畴结构可视为一种单指令图式编程语言Run，其唯一指令名为RUN。本版更新：调整标题，优化文本。（另新增大量习题与训练集，但因超出arXiv篇幅限制（早期版本已存在此问题），故“训练集”与“案例”部分暂被注释。）