Hypercomputation is a relatively new theory of computation which treats computing methods and devices that transcend the Church-Turing thesis. This book will provide a thorough description of the field of hypercomputation, covering all attempts at devising conceptual hypermachines and all new promising computational paradigms that may eventually lead to the construction of a hypermachine. Readers will reach a deeper understanding of what computability is and why the Church-Turing thesis poses an arbitrary limit to what actually can be computed. Hypercomputing is quite a novel idea, and therefore the book is interesting to the reader in its own right. The most significant features of the book, however, will be the descriptions of the various attempts of hypercomputation: from trial-and-error machines to the exploration of the human mind treated as a device with computational abilities. Hypercomputation: Computing Beyond the Church-Turing Barrier is fairly self-contained but requires a solid background in mathematics (calculus, discrete mathematics, algebra, and topology). Topics and Features: * Comprehensive examination of the hypercomputation field * In-depth presentation of the current status of computation and its potential * Philosophical and pragmatic approach to the limits of computation * The human mind treated as a device with computational abilities, and its possible implications * New, promising computing paradigms This state-of-the-art monograph will be of interest to those interested in exploring this exciting new branch of Computer Science. It will be of particular interest to academics, engineers, and researchers in Computer Science, Mathematics and Physics.