  We perform complete group classification of the general class of quasi linear
wave equations in two variables. This class may be seen as a broad
generalization of the nonlinear d'Alembert, Liouville, sin/sinh-Gordon and
Tzitzeica equations. In this way we derived a number of new genuinely nonlinear
invariant models with high symmetry properties. In particular, we obtain four
classes of nonlinear wave equations admitting five-dimensional invariance
groups. Applying the symmetry reduction technique we construct multi-parameter
families of exact solutions of those wave equations.
