This booklet, Algorithms and Automatic Computing Machines, gives some of the historical aspects of algorithms and goes on to outline the development of the theory of algorithms that has taken place in the twentieth century. In defining the term algorithm, the author considers the close relation between algorithms and computing machines. The reader will need no specific mathematical background beyond intermediate algebra, but he should be able to follow a rather complex train of logical thought.The author, B. A. TRAKHTENBROT, is Docent at the Penza Pedagogical Institute and has written several research papers in the field of mathematical logic.