This volume provides a detailed introduction to algebraic control for nonlinear systems. It is divided into two parts: necessary methodology and applications to control problems. The book develops an alternative linear-algebraic strategy based on the use of vector spaces over suitable fields of nonlinear functions. This algebraic perspective is complementary to, and parallel in concept with, its more celebrated differential-geometric counterpart and deals more easily with several important characteristics of nonlinear systems. It describes a wide range of results, some of which can be derived using differential geometry but many of which cannot. They include: classical and generalized realization in the nonlinear context; accessibility and observability recast within the linear-algebraic setting; and results for dynamic and static state and output feedback. This second edition has been completely revised with new text, examples and exercises.