Introduction to AdS-CFT

These lectures present an introduction to AdS-CFT, and are intended both for begining and more advanced graduate students, which are familiar with quantum field theory and have a working knowledge of their basic methods. Familiarity with supersymmetry, general relativity and string theory is helpful, but not necessary, as the course intends to be as self-contained as possible. I will introduce the needed elements of field and gauge theory, general relativity, supersymmetry, supergravity, strings and conformal field theory. Then I describe the basic AdS-CFT scenario, of ${\cal N}=4$ Super Yang-Mills's relation to string theory in $AdS_5\times S_5$, and applications that can be derived from it: 3-point functions, quark-antiquark potential, finite temperature and scattering processes, the pp wave correspondence and spin chains. I also describe some general properties of gravity duals of gauge theories.