This text presents a systematic exposition of techniques for constructing relaxation oscillations and methods for investigating stability properties of certain classes of systems with delay. The authors bring out some of the distinctive features that have no analogues in relaxation systems of ordinary differential equations. The exposition provides analysis of significant examples from biophysics, mathematical ecology and quantum physics that elucidate important patterns. Many unsolved problems are posed. The book should appeal to researchers and specialists interested in the theory and applications of relaxation oscillations.