This book is a self-contained introduction to the foundational quantum algorithms that shaped the development of quantum computation. After a brief introduction, it develops the quantum circuit model and the core concepts needed to understand quantum algorithms, while providing the necessary background in quantum mechanics and linear algebra in a self-contained way.

Building on this foundation, the book then guides the reader step by step through the major quantum algorithms. The presentation follows the historical development of the subject, which also corresponds to a progression from simpler ideas to more sophisticated ones. Each chapter represents a deliberate step upward in difficulty, strengthening the reader’s intuition and technical skill in preparation for more advanced algorithms.

Designed for flexibility, the chapters are as independent as possible, making this book ideal for an advanced taught course or recommended reading. This book can also be used as an accessible self-study guide for newcomers, and as a convenient reference for more experienced readers.

Dr. Renato Portugal is a full researcher at the National Laboratory for Scientific Computing (LNCC), Brazil. He received the Howard E. Brandt Best Paper Award in 2017. His previous appointments include visiting professor positions in the Department of Applied Mathematics and the Symbolic Computation Group at the University of Waterloo, and in the Department of Physics at Queen’s University in Kingston, as well as a researcher position at the Brazilian Center for Research in Physics, where he earned his doctoral degree. Dr. Portugal has published more than 150 articles in scientific journals and refereed proceedings, has a Google Scholar h-index of 31, and has authored four books. He has also developed seven software packages, including The Invar Package in 2007. He served as General Chair of the Workshop-School on Quantum Information and Computation (WECIQ 2010) and will serve as General Chair of the Brazilian Congress of Quantum Science and Technology (CBCTQ 2026).