  These lecture notes provide an introduction to recent advances in generative
modeling methods based on the dynamical transportation of measures, by means of
which samples from a simple base measure are mapped to samples from a target
measure of interest. Special emphasis is put on the applications of these
methods to Monte-Carlo (MC) sampling techniques, such as importance sampling
and Markov Chain Monte-Carlo (MCMC) schemes. In this context, it is shown how
the maps can be learned variationally using data generated by MC sampling, and
how they can in turn be used to improve such sampling in a positive feedback
loop.
