With the help of the concept of the scattering matrix S, reactions in quantum mechanics can be described in a very general form. If one has a theory for calculating the matrix elements, the relationship between these matrix elements and the physical observables such as the cross section and the decay rate is of particular interest. This is what we will initially focus on. Independently of a specific theory, the S-matrix must satisfy certain symmetry conditions, which alone are sufficient to determine the form of the cross section. The most well-known example is the relationship between particle spins and angular distribution. Therefore, following the formulas for cross sections and decay rates, the concept of symmetry will be introduced. The subsequent sections deal with the symmetries of the scattering matrix and the resulting experimental consequences.