This self-contained monograph addresses the flow equation approach to many-particle systems. The flow equation approach consists of a sequence of infinitesimal unitary transformations and is conceptually similar to renormalization and scaling methods. Flow equations provide a framework for analyzing Hamiltonian systems where these conventional many-body techniques fail. The text first discusses the general ideas and concepts of the flow equation method. In a second part these concepts are illustrated with various applications in condensed matter theory including strong-coupling problems and non-equilibrium systems. The monograph is accessible to readers familiar with graduate-level solid-state theory.