Sections and metrics are well known and are very important objects in graph theory, combinatorial optimization problems, and in general in discrete mathematics. They appear in other areas of mathematics and its applications, such as metric geometry, number geometry, combinatorial matrix theory, flowchart theory, quantum mechanics, statistical physics, analysis, and probability theory. This book is conceived as a textbook and guide for researchers, graduate students and students interested in discrete mathematics and its relationships with other areas of mathematics or its applications.