This book provides a treatment of the theory of quantum groups (quantized universal enveloping algebras and quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The theory of the simplest and most important quantum groups and their representations is presented in detail. A number of topics and results from the more advanced general theory are developed and discussed. Many applications in mathematical and theoretical physics are indicated. The book starts as an introduction for...