This volume contains papers based on invited talks given at the 2005 IMA SummerWorkshop on Wireless Communications, held at the Institute for Mathematics and Its Applications, University of Minnesota, June 22 - July 1, 2005. The workshop provided a great opportunity to facilitate the communications between academia and the industry, and to bridge the mathematical sciences, engineering, information theory, and communication communities. The emphases were on design and analysis of computationally efficient algorithms to better understand the behavior and to control the wireless telecommunication networks. As an achieve, this volume presents some of the highlights of the workshop, and collects papers covering a broad spectrum of important and pressing issues in wireless communications. All papers have been reviewed. One of the book's distinct features is highly multi-disciplinary. This book is useful for researchers and advanced graduate students working in communication networks, information theory, signal processing, and applied probability and stochastic processes, among others.