  In this review, we have reached from the most basic definitions in the theory
of groups, group structures, etc. to representation theory and irreducible
representations of the Poincar'e group. Also, we tried to get a more
comprehensible understanding of group theory by presenting examples from the
nature around us to examples in mathematics and physics and using them to
examine more important groups in physics such as the Lorentz group and
Poincar'e group and representations It is achieved in the physical fields that
are used in the quantum field theory.
