  This is an introduction to models of accretion discs around black holes.
After a presentation of the non-relativistic equations describing the structure
and evolution of geometrically thin accretion discs we discuss their
steady-state solutions and compare them to observation. Next we describe in
detail the thermal-viscous disc instability model and its application to dwarf
novae for which it was designed and its X-ray irradiated-disc version which
explains the soft X--ray transients, i.e. outbursting black-hole low-mass X-ray
binaries. We then turn to the role of advection in accretion flows onto black
holes illustrating its action and importance with a toy model describing both
ADAFs and slim discs. We conclude with a presentation of the
general-relativistic formalism describing accretion discs in the Kerr
space-time.
