  In this paper intermodal modulational instability (IM-MI) is analyzed in a
multimode fiber where several spatial and polarization modes propagate. The
coupled nonlinear Schr\"{o}dinger equations describing the modal evolution in
the fiber are linearized and reduced to an eigenvalue problem. As a result, the
amplification of each mode can be described by means of the eigenvalues and
eigenvectors of a matrix that stores the information about the dispersion
properties of the modes and the modal power distribution of the pump. Some
useful analytical formulas are also provided that estimate the modal
amplification as function of the system parameters. Finally, the impact of
third-order dispersion and of absorbtion losses is evaluated, which reveals
some surprising phenomena into the IM-MI dynamics. These outcomes generalize
previous studies on bimodal-MI, related to the interaction between 2 spatial or
polarization modes, to the most general case of $N>2$ interacting modes.
Moreover, they pave the way towards the realization of wideband multimode
parametric amplifiers
