This book integrates both classical and modern treatments of difference equations. It contains the most updated material as well as a large set of applications to a variety of disciplines. Scientists and engineers who are interested in discrete mathematical models will find it useful as a reference. The presentation is also simple enough for use by advanced undergraduates. This second edition includes new sections on applications to mathematical biology, Birkhoff's theory, continued fractions and orthogonal polynomials, and many revised exercises.