This book presents hypergraph theory in its entirety; all definitions are introduced as simply as possible, yet rigorously, to highlight the theory’s coherence. Hypergraph theory is one of the most dynamic theories of recent years. This stems from the applications of hypergraphs in all areas of human activity. These structures are found in mathematics, engineering, and the humanities. This book presents hypergraph theory in its entirety; all definitions are introduced as simply as possible, yet rigorously, to highlight the theory’s coherence. A significant portion of the chapters develops original results, particularly in topology and algebra. Their originality and novelty aim to help readers better understand hypergraphs in all their diversity, so they can perceive their relevance as mathematical tools. This book is a valuable resource for advanced students in computer science and mathematics. It was used as an annual master’s level course for many years, making it also perfectly suited for master’s students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It is also be useful to scientists, engineers, and anyone wishing to deepen their understanding of hypergraph theory.