Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object.One renewed motivation for studying this subject, which has developed for almost 50 years in many directions, comes from quantum field theory, especially string theory, where topological invariants play an important role.