Mathematician Harald Bohr, motivated by questions about which functions could be represented by a Dirichlet series, devised the theory of almost periodic functions during the 1920s. His groundbreaking work influenced many later mathematicians, who extended the theory in new and diverse directions. In this volume, Bohr focuses on an essential aspect of the theory — the functions of a real variable — in full detail and with complete proofs. The treatment, which is based on Bohr's lectures, starts with an introduction that leads to discussions of purely periodic functions and their Fourier series. The heart of the book, his exploration of the theory of almost periodic functions, is supplemented by two appendixes that cover generalizations of almost periodic functions and almost periodic functions of a complete variable.