  After a brief introduction to the sixteenth and seventeenth century views of
the Universe and the nineteenth century paradox of Olbers, we start the history
of the cosmic expansion with Hubble's epochal discovery of the recession
velocities of spiral galaxies. By then Einstein's theories of relativity were
well known, but no suitable metric was known. Prior to introducing General
Relativity we embark on a non-chronological derivation of the Robertson-Walker
metric directly from Special Relativity and the Minkowski metric endowed with a
Gaussian curvature. This permits the definition of all relativistic distance
measures needed in observational astronomy. Only thereafter do we come to
General Relativity, and describe some of its consequences: gravitational
lensing, black holes, various tests, and the cornerstone of the standard Big
Bang model, the Friedmann-Lemaitre equations. Going backwards in time towards
Big Bang we first have to trace the thermal history, and then understand the
needs for a cosmic inflation and its predictions. The knowledge of the Big Bang
model is based notably on observations of the Cosmic Microwave Background
Radiation, large scale structures, and the redshifts of distant supernovae.
They tell us that gravitating matter is dominated by a dark and dissipationless
component of unknown composition, and that the observable part of the Universe
exhibits an accelerated expansion representing a fraction of the energy even
larger than gravitating matter.
