Massive astrophysical bodies such as forming stars or compact objects exert gravitational attraction onto the gas at rest in their surroundings. However, owing to the conservation of its angular momentum, the cosmic material falling in the gravitational well undergoes rapid rotation and, after the loss of the potential energy released in this process through radiation, tends to form a disc. In discs formed of sufficiently cool gas, the gravitational attraction of the central body is at first approximation balanced by centrifugal forces - as in planetary systems. Such discs are found in a variety of astrophysical environments: around young stars where they are the sites of planetary formation, around super-massive black holes in the centre of active galaxies and around the compact stars that disrupt their companion in interacting binary systems. Interestingly, some dissipative processes acting within the disc can drive a net radial transport of angular momentum outwards by modifying the radial balance. As a consequence of the removal of its angular momentum, the gas in rotation within the disc is accreted by the central body, i.e. it falls in further towards the centre of the disc and feeds the proto-star or compact object that produces the gravitational field. Furthermore, the gravitationally stratified gas that forms the accretion disc can be partially or totally conducting electricity and can therefore interact with external magnetic fields (e.g. with that of a central star or large-scale jets) and with magnetic fields embedded within the disc. So, modelling the extremely rich and complex dynamics of accretion discs, which is central to modern astrophysics, calls for in-depth understanding of the physics and mathematics of rotating and conducting stratified fluids.