Historically, the theory of stability is based on linear differential systems, which are simple and important systems in ordinary differential equations. The research on differential equations and on the theory of stability will, to a certain extent, be influenced by the research on linear differential systems. For differential linear equation systems, there are still many historical open questions attracting mathematicians. This text deals with the theory of linear differential systems developed around the notion of exponential dichotomies. The first author advanced the theory of stability through his research in this field. Several important results on linear differential systems are presented. They concern exponential dichotomy and the structure of the sets of hyperbolic points. The book contains five chapters. Chapter One introduces some necessary classical results on the linear differential systems, and the following chapters discuss exponential dichotomy, spectra of almost periodic linear systems, the Floquet theory for quasi periodic linear systems and the structure of sets of hyperbolic points. The book should be useful as a reference in the area of the stability theory of ordinary differential equations and the theory of dynamic systems.