Singularities and the classification of 1-forms and Pfaffian equations are interesting not only as classical problems, but also because of their applications in contact geometry, partial differential equations, control theory, nonholonomic dynamics, and variational problems. In addition to collecting results on the geometry of singularities and classification of differential forms and Pfaffian equations, this monograph discusses applications and closely related classification problems. Zhitomirskiĭ presents proofs with all results and ends each chapter with a summary of the main results, a tabulation of the singularities, and a list of the normal forms. The main results of the book are also collected together in the introduction.