Introduction

Gravitational lenses are a powerful tool for Astrophysics and Cosmology. The goals of this project are: i) to obtain a robust determination of the Hubble constant from the time delay measured between the images of a lensed quasar; ii) to study the individual and statistical properties of dark matter condensations in lens galaxies from microlensing on the images of lensed quasars; iii) to study the unresolved structure of quasars (broad and narrow emission line and continuum emission regions) from induced variations by microlensing in the photometry of the lensed quasar images as well as in the profile of their emission lines; iv) to study the variation of dust extinction properties with redshift from the determination of extinction curves in lens galaxies; (v) to develop new numerical and statistical methods to study microlensing and (vi) to detect exoplanets through gravitational microlensing.