This book integrates both classical & modern treatments of difference equations. It contains the most updated & comprehensive material on stability, Z-transform, discrete control theory & asymptotic theory, continued fractions & orthogonal polynomials. Yet the presentation is simple enough for the book to be used by advanced undergraduate & beginning graduate students in mathematics, engineering science & economics. Moreover, scientists & engineers who are interested in discrete mathematical models will find it useful as a reference. The book contains a large set of applications in a variety of disciplines, including neural networks, feedback control, Markov chains, trade models, heat transfer, propagation of plants, epidemic models & host-parasitoid systems. Each section ends with an extensive & highly selected set of exercises.