This is a textbook intended for students and researchers who wish to under­ stand the physics of standard "big bang" cosmology and how it is used to interpret the most recent observations. It is based on courses given over the last seven years to beginning graduate students at the University of Paris and to advanced undergraduates at lEcole Poly technique. Since the great major­ ity of these students did not intend to become professional cosmologists, I have emphasized subjects that should be of general interest. Progress in observations over the last ten years has been truly astounding and a new textbook might be justified simply to report on recent break­ throughs. The traditional successes of modern cosmology are well-known. Among these are the dynamical understanding of the universal expansion, the prediction of the cosmic microwave background radiation, and the calculation of the abundances of the light elements. To these we can add new observa­ tions that suggest that we are beginning the era of "precision cosmology." Perhaps most spectacular was the observation this year of the first acoustic peak in the anisotropy spectrum of the cosmic background radiation by the Boomerang and Maxima collaborations. These beautiful measurements have convinced many people that the universe has a nearly critical energy density and that a complete understanding of structure formation may be at hand.