  We have derived the mean proper motions and space velocities of 154 Galactic
globular clusters and the velocity dispersion profiles of 141 globular clusters
based on a combination of Gaia DR2 proper motions with ground-based
line-of-sight velocities. Combining the velocity dispersion profiles derived
here with new measurements of the internal mass functions allows us to model
the internal kinematics of 144 clusters, more than 90% of the currently known
Galactic globular cluster population. We also derive the initial cluster masses
by calculating the cluster orbits backwards in time applying suitable recipes
to account for mass loss and dynamical friction. We find a correlation between
the stellar mass function of a globular cluster and the amount of mass lost
from the cluster, pointing to dynamical evolution as one of the mechanisms
shaping the mass function of stars in clusters. The mass functions also show
strong evidence that globular clusters started with a bottom-light initial mass
function. Our simulations show that the currently surviving globular cluster
population has lost about 80% of its mass since the time of formation. If
globular clusters started from a log-normal mass function, we estimate that the
Milky Way contained about 500 globular clusters initially, with a combined mass
of about $2.5 \cdot 10^8$ $M_\odot$. For a power-law initial mass function, the
initial mass in globular clusters could have been a factor of three higher.
