Group theory and irreducible representations of the Poincare group

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.