In a simple but mathematically coherent manner, this text examines the basis of the distribution theories devised by Schwartz and by Mikusinki. Rigorous and concise, it surveys the functional theory of distributions as well as the algebraic theory. Its easy generalizations offer applications to a wide variety of problems. The two-part treatment begins with the functional theory of distributions, exploring differentiation, formation of products, translation and regularization, convergence, Fourier transforms, and partial differential equations. The second half focuses on the algebraic theory of distributions, with discussions of derivatives and integrals, differential and integral equations, relations to the Laplace transform, convergence, translation and the exponential function, and partial differential equations. Geared to students of mathematics, this text will also prove instructive to physicists and applied scientists.