White dwarf stars, compact objects with extremely high interior densities, are the most common end product in the evolution of stars. In this paper we review the history of their discovery, and of the realisation that their structure is determined by the physics of the degenerate electron gas. Spectral types and surface chemical composition show a complicated pattern dominated by diffusion processes and their interaction with accretion, convection and mass loss. While this interaction is not completely understood in all its detail at present, the study may ultimately lead to important constraints on the theory of stellar evolution in general. Variability, caused by non-radial oscillations of the star, is a common phenomenon and is shown to be a powerful probe of the structure of deeper layers that are not directly accessible to observation. Very strong magnetic fields detected in a small fraction of white dwarfs offer a unique opportunity to study the behaviour of atoms under conditions that cannot be simulated in terrestrial laboratories.

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