  This is an introductory review of the AdS/CFT correspondence and of the ideas
that led to its formulation. We show how comparison of stacks of D3-branes with
corresponding supergravity solutions leads to dualities between conformal large
$N$ gauge theories in 4 dimensions and string backgrounds of the form
$AdS_5\times X_5$ where $X_5$ is an Einstein manifold. The gauge invariant
chiral operators of the field theory are in one-to-one correspondence with the
supergravity modes, and their correlation functions at strong `t Hooft coupling
are determined by the dependence of the supergravity action on AdS boundary
conditions. The simplest case is when $X_5$ is a 5-sphere and the dual gauge
theory is the ${\cal N}=4$ supersymmetric SU(N) Yang-Mills theory. We also
discuss D3-branes on the conifold corresponding to $X_5$ being a coset space
$T^{1,1}=(SU(2)\times SU(2))/U(1)$. This background is dual to a certain ${\cal
N}=1$ superconformal field theory with gauge group $SU(N)\times SU(N)$.
