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This book provides a relatively complete introduction to the methods used in computational condensed matter. A wide range of electronic structure theories are introduced, including traditional quantum chemistry methods, density functional theory, many-body perturbation theory, and more. Molecular dynamics simulations are also discussed, with extensions to enhanced sampling and free-energy calculation techniques including umbrella sampling, meta-dynamics, integrated tempering sampling, etc. As a further extension beyond the standard Born-Oppenheimer molecular dynamics, some simulation techniques for the description of quantum nuclear effects are also covered, based on Feynman's path-integral representation of quantum mechanics. The book aims to help beginning graduate students to set up a framework of the concepts they should know before tackling the physical/chemical problems they will face in their research.