This chapter considers some simple physical examples, and discusses the solutions of a series of problems which cannot be investigated without using the analytic properties. The development of the theoretical and experimental aspects of the physics of strongly interacting particles has required the creation of theoretical methods. One of these methods is based on the analytic properties of physical quantities, for instance the analytic properties of the scattering amplitude as a function of energy and scattering angle. In cases where the quantity in question has a singularity in the complex plane near the real axis, its behaviour on the real axis is determined by the character of this singularity. In the complex plane of the parameters physical functions may have various singularities; in each case there must be physical reasons for their appearance. The chapter draws important conclusions about the relations between different physical quantities.