These topics are: the magnetopause (topology and microscopic theories of structure, dynamical effects due to interplanetary magnetic fields and solar-wind pressure changes), the plasmasphere (topology, theories of origin, time variations, plasmaphysical processes), the proton radiation belt (origin, theory of particle motion in the geomagnetic field using invariants), wave-particle interaction (simplified theory, experimental verification), the electron radiation belt (origin, transport, losses), excitation of waves (velocity space instabilities, applications and experimental verification), aurorae (origin, plasmaphysical effects associated with barium cloud releases in the ionosphere), the plasmamantle and the plasmasheet (topology, possible connection between the two phenomena), and finally a brief overview of magnetospheres in the Solar System which have been accessible to 'in situ' investigation using space probes.