This is an updated, revised and extended translation from the Russian original work Symmetry Analysis and Exact Solutians of Equations of Nonlinear Mathematical Physics, Nauk:a, Kiev, © 1989 AU Rights Reserved

New Lie and conditional symmetries of nonlinear diffusion equations with convection terms are constructed. Examples of new ansätze and exact solutions for some nonlinear equations (in particular, for the Murray and the Newell–Whitehead equations) are presented.

New Lie symmetry classification of the known class of reaction-diffusion-convection equations is presented. The classification method is based on combining the standard group classification method and the form-preserving transformation approach.

Multiparametrical exact solutions of the many-dimensional nonlinear d'Alembert, Liouville, sine-Gordon and eikonal equations arc obtained. The maximally extensive local invariance groups of the equations are determined and invariants of the extended Poincaré group are found.

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