  A conduction electron (or hole) together with its self-induced polarisation
in a polar semiconductor or an ionic crystal forms a quasi-particle, which is
called a polaron. The polaron concept is of interest, not only because it
describes the particular physical properties of charge carriers in polarizable
solids but also because it constitutes an interesting field theoretical model
of a fermion interacting with a scalar boson field. The early work on polarons
was concerned with general theoretical formulations and approximations, which
now constitute the standard polaron theory, and with experiments on cyclotron
resonance and transport properties. Because of the more recent interest in the
two-dimensional electron gas, the study of the polaron in two dimensions became
important. Again cyclotron resonance, and therefore the behaviour of polarons
in magnetic fields, was a key issue. When two electrons (or two holes) interact
with each other simultaneously through the Coulomb force and via the
electron-phonon-electron interaction, either two independent polarons can occur
or a bound state of two polarons - a bipolaron - can arise. Bipolarons have
been considered to possibly play a role in high-Tc superconductivity. The
polaron concept has been extended to several systems where one or many fermions
interact with a bath of bosons, e. g., small polaron, piezopolaron, polaronic
exciton, spin - or magnetic - polaron, "ripplonic polaron", "plasmaron",
"hydrated polarons" etc.
