The book deals with the symptotic analysis of relaxation oscillations, which are nonlinear oscillations characterized by rapid change of a variable within a short time interval of the cycle. The type of asymptotic approximation of the solution is known as the method of matched asymptotic expansions. In case of coupled oscillations it gives conditions for entrainment. For spatially distributed oscillators phase wave solutions can be constructed. The asymptotic theory also covers the chaotic dynamics of free and forced oscillations. The influence of stochastic perturbations upon the period of the oscillation is also covered. It is the first book on this subject which also provides a survey of the literature, reflecting historical developments in the field. Furthermore, relaxation oscillations are analyzed using the tools drawn from modern dynamical system theory. This book is intended for graduate students and researchers interested in the modelling of periodic phenomena in physics and biology and will provide a second knowledge of the application of the theory of nonlinear oscillations to a particular class of problems.