In this paper we have proposed and studied the following 3 basic problems in beam propagation: 1) defination of beam quality and its measurements; 2) arbitrary beam propagation through real optical systems and 3) nonlinear propagation of real laser beams. Here, we are interested in the methods to solve these problems. We have analytically investigated the beam quality by assuming the phase aberrations as Gaussian random variables.For the nonlinear harmonic conversion of real laser beams, we have developed a theory by applying the spatial spectrum analysis to the nonlinear coupling.