Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject.

图灵1936年的著名论文介绍了计算机器的正式定义，图灵机器。这个模型导致了实际计算机和可计算性理论的发展，即研究机器可以和不能计算的东西。这本书介绍了从图灵和Post到当前结果和方法的经典可计算性理论，以及它们在研究代数结构、模型的信息内容中的应用，以及它们与Peano算法的关系。作者将这门学科描述为一门需要实践的艺术，一门所有数学家在他们的学科中都认识到的内在美的美学意义上的艺术。