In 1836 and 1837, Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which began the subject now known as the Sturm-Liouville theory. In 1910, Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, Sturm-Liouville theory has remained an intensely active field of research with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of research on some aspects of this theory. Prerequisites for using the book are a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory. The book has an extensive list of references and examples and numerous open problems. Examples include classical equations and functions associated with Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, and Morse; also included are examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples. This book offers a well-organized viewpoint on some basic features of Sturm-Liouville theory. With many useful examples treated in detail, it will make a fine independent study text and is suitable for graduate students and researchers interested in differential equations.