This text offers a uniquely application-oriented introduction to the theory of distributions. It presents distributions as a natural method of analysis from both a mathematical and physical point of view. The discussion emphasizes applications to the general study of differential equations and in particular, linear partial differential equations. In this book the subject is motivated by many exercises, hints and solutions that guide the student along a path requiring only a minimal mathematical background. Advanced undergraduate and graduate students in mathematics, theoretical physics and engineering will find this textbook a welcome introduction to the theory of distributions, a subject often requiring a strong mathematical background.