Hypergraphs are systems of finite sets and form, probably, the most general concept in discrete mathematics. This branch of mathematics has developed very rapidly during the latter part of the twentieth century, influenced by the advent of computer science. Many theorems on set systems were already known at the beginning of the twentieth century, but these results did not form a mathematical field in itself. It was only in the early 1960s that hypergraphs become an independent theory. Hence, hypergraph theory is a recent theory. It was mostly developed in Hungary and France under the leadership of mathematicians like Paul Erdös, László Lovász, Paul Turán,… but also by C. Berge, for the French school. Originally, developed in France by Claude Berge in 1960, it is a generalization of graph theory. The basic idea consists in considering sets as generalized edges and then in calling hypergraph the family of these edges (hyperedges). As extension of graphs, many results on trees, cycles, coverings, and colorings of hypergraphs will be seen in this book.