This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text. AUTHOR: David A. Sanchez received his PhD in Mathematics from the University of Michigan in 1964. He taught at several universities, including UCLA, the University of Wisconsin, and the University of New Mexico, and he held various administrative positions in academia and elsewhere, including with the National Science Foundation and the Los Alamos National Laboratory. Dr. Sanchez is the author of several books on aspects of ordinary differential equations.