In the talk, I will present a gentle and accessible introduction to the mathematically rigorous approach to the perturbative quantum field theory developed by Epstein and Glaser. The fundamental objects of this approach are the time-ordered products of polynomials in the basic fields which are defined axiomatically. Their construction is carried out in the position space and does not require the introduction of any ultraviolet regularization. Using the time-ordered products, one first defines the scattering matrix and the interacting fields in the theory in which the coupling constant is replaced by a Schwartz function called the switching function. In order to obtain the physical scattering matrix and interacting fields the so-called adiabatic limit is taken.