This monograph is dedicated to so-called singularly perturbed equations, including nonlinear ordinary differential equations, integro-differential equations, and differential-difference equations. These are equations that contain a small parameter undergoing degeneration—such as a reduction in order—when the parameter is set to zero. The book offers a systematic and unified presentation of the theory behind these types of equations, a subject that until recently was mainly available only in journal articles. Readers are introduced to an algorithm for constructing asymptotic expansions of solutions to various problems involving such equations. The method is straightforward and practical, making it accessible for real-world applications. Intended for researchers and students working with asymptotic methods, this book also holds interest for physicists, mechanics, and engineers. The core results are accessible to those with a solid mathematical background from technical universities.