  I give an account of the definitions of parton densities, both the
conventional ones, integrated over parton transverse momentum, and unintegrated
transverse-momentum-dependent densities. The aim is to get a precise and
correct definition of a parton density as the target expectation value of a
suitable quantum mechanical operator, so that a clear connection to
non-perturbative QCD is provided. Starting from the intuitive ideas in the
parton model that predate QCD, we will see how the simplest operator
definitions suffer from divergences. Corrections to the definition are needed
to eliminate the divergences. An improved definition of unintegrated parton
densities is proposed.
