  It is shown that the novel Lie group of transformations method is a competent
and prominent tool in solving nonlinear partial differential equations(PDEs) in
mathematical physics. Lie group analysis is used to carry out the similarity
reduction and exact solutions of the (3 + 1)-dimensional
Calogero-Bogoyavlenskii-Schiff (CBS) equation. This research deals with the
similarity solutions of CBS equation. We have obtained the infinitesimal
generators, commutator table of Lie algebra, symmetry group and similarity
reduction for the CBS equation. For the different Lie algebra, Lie symmetry
method reduced (3 + 1)-dimensional CBS equation into new (2 + 1)-dimensional
partial differential equations and again using Lie symmetry method these PDEs
are reduced into various ordinary differential equations(ODEs).
