The calculation of transport properties of Fermi liquids, based on the formalism developed by Abrikosov and Khalatnikov, requires the knowledge of the probability of collisions between quasiparticles in the vicinity of the Fermi surface. We have carried out a study of the shear viscosity of pure neutron matter, whose value plays a pivotal role in determining the stability of rotating neutron stars, in which these processes are described using a state-of-the-art nucleon-nucleon potential. Medium modifications of the scattering cross section have been consistently taken into account through an effective interaction obtained from the matrix elements of the bare interaction between correlated states. Medium effects produce a large increase of the viscosity at densities rho > or approximately0.1 fm;{-3}.