This booklet serves as an introduction to Kleene Algebra (KA), a set of laws that can be used to study general equivalences between programs. It discusses how general programs can be modeled using regular expressions, how those expressions correspond to automata, and how this correspondence can be exploited to obtain the central result of KA, namely that an equivalence of regular expressions is true if and only if it can be proved using the laws of KA. Each chapter closes with a set of exercises to further build intuition and understanding, and there is an optional chapter that develops automata theory through the lens of coalgebra.

翻译：本手册旨在介绍Kleene代数（KA），这是一组可用于研究程序间一般等价关系的定律。它探讨了如何利用正则表达式对通用程序进行建模，这些表达式如何与自动机对应，以及如何利用这种对应关系来获得KA的核心结论：一个正则表达式的等价性成立，当且仅当可以通过KA的定律予以证明。每章末尾附有习题集，以进一步培养直觉与理解；另设有一个可选章节，从余代数的视角发展自动机理论。