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This book is an introduction to graph theory, presenting most of its elementary and classical notions through an original and rigorous approach, including detailed proofs of most of the results. It covers all aspects of graph theory from an algebraic, topological and analytic point of view, while also developing the theory’s algorithmic parts. The variety of topics covered aims to lead the reader in understanding graphs in their greatest diversity in order to perceive their power as a mathematical tool. The book will be useful to undergraduate students in computer science and mathematics as well as in engineering, but it is also intended for graduate students. It will also be of use to both early-stage and experienced researchers wanting to learn more about graphs.