Wigner's classification of elementary particles is a fundamental achievement in quantum theory. It begins by providing a framework for quantum theory and addresses the question of how observers can agree on the identity of a particle, regardless of their position in space and time. The discussion covers key aspects of quantum mechanics, including Hermitian operators and their connection to observables, as well as the interpretation of the wave function's squared magnitude as probability. Symmetries in quantum mechanics are explored, with a focus on unitary (or antiunitary) operators that conserve probability. Additionally, the relevance of the Poincaré group's Lie algebra, which describes the properties of particles unaffected by Lorentz transformations, is examined. Wigner's significant contribution involves using irreducible representations of the little group to describe the entire group, simplifying the process. Through the application of symmetries, group theory, Einstein's special theory of relativity, and irreducible representations of the little group, Wigner concludes that observers in any space-time location can agree on a particle's identity by measuring and comparing its mass and spin. This result has had a profound impact on the development of theoretical frameworks in modern physics, such as quantum field theory and the standard model of elementary particles, proving its significance.