Whatis "topological" about topological quantum states? How many types oftopological quantum phases are there? What is a zero-energy Majoranamode, how can it be realized in a solid state system, and how can it beused as a platform for topological quantum computation? What is quantumcomputation and what makes it different from classical computation?Addressing these and other related questions,Introduction to Topological Quantum Matter & Quantum Computationprovides an introduction to and a synthesis of a fascinating andrapidly expanding research field emerging at the crossroads of condensedmatter physics, mathematics, and computer science. Providing the bigpicture, this book is ideal for graduate students and researchersentering this field as it allows for the fruitful transfer of paradigmsand ideas amongst different areas, and includes many specific examplesto help the reader understand abstract and sometimes challengingconcepts. It explores the topological quantum world beyond thewell-known topological insulators and superconductors and emphasizes thedeep connections with quantum computation. It addresses key principlesbehind the classification of topological quantum phases and relevantmathematical concepts and discusses models of interacting andnoninteracting topological systems, such as the torric code and thep-wave superconductor. The book also covers the basic properties ofanyons, and aspects concerning the realization of topological states insolid state structures and cold atom systems.Quantumcomputation is also presented using a broad perspective, which includesfundamental aspects of quantum mechanics, such as Bell's theorem, basicconcepts in the theory of computation, such as computational models andcomputational complexity, examples of quantum algorithms, and elementsof classical and quantum information theory.