  In this work we present, for the first time, the non-perturbative
renormalization for the unpolarized, helicity and transversity quasi-PDFs, in
an RI' scheme. The proposed prescription addresses simultaneously all aspects
of renormalization: logarithmic divergences, finite renormalization as well as
the linear divergence which is present in the matrix elements of fermion
operators with Wilson lines. Furthermore, for the case of the unpolarized
quasi-PDFs, we describe how to eliminate the unwanted mixing with the twist-3
scalar operator. We utilize perturbation theory for the one-loop conversion
factor that brings the renormalization functions to the MS-scheme at a scale of
2 GeV. We also explain how to improve the estimates on the renormalization
functions by eliminating lattice artifacts. The latter can be computed in
one-loop perturbation theory and to all orders in the lattice spacing. We apply
the methodology for the renormalization to an ensemble of twisted mass fermions
with Nf=2+1+1 dynamical light quarks, and a pion mass of around 375 MeV.
