"Communications in Nonlinear Science and Numerical Simulation'' is given entirely to appreciation of applications of Lie groups to nonlinear problems in acoustics, engineering, biomedicine, etc. The selection of papers covers the following topics: a) group classification of differential equations and optimal systems of invariant and partially invariant solutions including classification of differential equations according to their symmetries; b) equivalence groups and invariants of families of differential equations; c) symmetries of delay equations; d) symmetries of stochastic differential equations; e) application to nonlinear physics and biomathematics. We hope that this special issue highlights the recent major developments in this fascinating field of mathematics and mathematical modelling.