  The main result of this research Monograph is the existence of small
amplitude time quasi-periodic solutions for autonomous nonlinear wave equations
$$ u_{tt} - \Delta u + V(x) u + g(x, u) = 0 \, , \quad x \in T^d \, , \quad g
(x,u) = a(x) u^3 + O(u^4 ) , $$ in any space dimension and with a
multiplicative potential. The proof is based on a Nash-Moser implicit function
scheme. A key step is the construction of an approximate right inverse of the
linearized operators obtained at any step of the iteration. In order to avoid
the difficulty posed by the violation of the second order Melnikov
non-resonance conditions we develop a multiscale inductive approach \'a la
Bourgain. A feature of the Monograph is to present the proofs, techniques and
ideas developed in a self-contained and expanded manner.
