Correspondence between supersymmetric Yang-Mills and supergravity theories

The AdS/CFT correspondence establishes a relationship between supersymmetric gravity (SUGRA) on anti-de Sitter (AdS) space and supersymmetric Yang-Mills (SYM) theory, which is a conformally invariant field theory (CFT). The AdS space is the solution of the Einstein-Hilbert equations with a constant negative curvature. Why is this relationship important? What kind of relationship is this? How does one find it? The purpose of this paper is to answer these questions. We try to present the main ideas and arguments underlying this relationship, starting with a brief sketch of 'old' string theory results and proceeding with the definition of D-branes and a description of their main features. A demonstration of the discussed correspondence and arguments in it its favor conclude the paper.