??The theory behind the implementation of a numerical solver for the generalized multimode nonlinear Schroedinger equation (GMMNLSE) modeling the propagation of a modulated electromagnetic field in a fiber subject to linear and nonlinear effects is presented. ?? ??Firstly, the mode-independent linear effects up to second-order in frequency are reviewed. Secondly, particular attention is devoted to the two polarization mode case where the linear effects arising from fiber perturbations are referred to as polarization mode dispersion (PMD). The understanding of PMD phenomena is basic for the study of linear and nonlinear phenomena in the higher-dimensional multimode case. Within the framework of PMD, a segment of uniformly perturbed fiber is initially considered, both for frequency-independent and frequency-dependent birefringence.