  The Holstein Molecular Crystal Model is investigated by a strong coupling
perturbative method which, unlike the standard Lang-Firsov approach, accounts
for retardation effects due to the spreading of the polaron size. The effective
mass is calculated to the second perturbative order in any lattice
dimensionality for a broad range of (anti)adiabatic regimes and electron-phonon
couplings. The crossover from a large to a small polaron state is found in all
dimensionalities for adiabatic and intermediate adiabatic regimes. The phonon
dispersion largely smooths such crossover which is signalled by polaron mass
enhancement and on site localization of the correlation function. The notion of
self-trapping together with the conditions for the existence of light polarons,
mainly in two- and three-dimensions, are discussed. By the imaginary time path
integral formalism I show how non local electron-phonon correlations, due to
dispersive phonons, renormalize downwards the {\it e-ph} coupling justifying
the possibility for light and essentially small 2D Holstein polarons.
