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This book is intended to be an introductory material on topological quantum codes, with the necessary elements from a mathematical and engineering point of view, aimed at postgraduate or undergraduate students at more advanced level, in the courses of Mathematics, Engineering, or Computing. As an introduction to this book, this chapter presents, in general terms, the central concepts of quantum computing and how it was developed through a historical overview. Then, the error-correcting quantum code models are highlighted, up to the topological quantum codes, according to the chronology, thus giving an overview of this research area and what will be covered during the other chapters of the book.