Combinatorial geometry is a young branch of mathematics, formed in an independent direction only in the 20th century. Its origin is associated with the works of Khedive, Badger, Hadwiger, South, Grnbaum, Sekefalvi Nay and other mathematicians. This monograph is the first large study of Soviet scientists on combinatorial geometry . It differs from existing books on combinatorial geometry by a large number of new task formulations and obtained results. The use of different understandings of the bulge allows us to understand the classical theorems of combinatorial geometry in a different way, gives a number of new results and formulations of problems. The book is intended for researchers in the field of geometry, teachers of universities and pedestals, graduate students, and can also be useful for mathematics students when choosing topics for course and thesis works and as material for special courses and seminars .