In a comprehensive introduction to the qualitative theory of ordinary differential equations, Barreira and Valls (both mathematics, Instituto Superior Técnico, Portugal) focus on the existence and uniqueness of solution, phase portraits, linear equations and their perturbations, stability and Lyapunov functions, hyperbolicity, and equations in the plane. The book can support a second course on ordinary differential equations, but has enough material to be used several different ways as well, such as advanced graduate courses on stability or hyperbolicity. The Portuguese edition, Equações diferenciais: Teoria Qualitativa, was published by IST Press in 2010, and was translated by the authors. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)