  Abridged. White dwarf stars are the final evolutionary stage of the vast
majority of stars, including our Sun. The study of white dwarfs has potential
applications to different fields of astrophysics. In particular, they can be
used as independent reliable cosmic clocks, and can also provide valuable
information about the fundamental parameters of a wide variety of stellar
populations, like our Galaxy and open and globular clusters. In addition, the
high densities and temperatures characterizing white dwarfs allow to use these
stars as cosmic laboratories for studying physical processes under extreme
conditions that cannot be achieved in terrestrial laboratories. They can be
used to constrain fundamental properties of elementary particles such as axions
and neutrinos, and to study problems related to the variation of fundamental
constants.
  In this work, we review the essentials of the physics of white dwarf stars.
Special emphasis is placed on the physical processes that lead to the formation
of white dwarfs as well as on the different energy sources and processes
responsible for chemical abundance changes that occur along their evolution.
Moreover, in the course of their lives, white dwarfs cross different
pulsational instability strips. The existence of these instability strips
provides astronomers with an unique opportunity to peer into their internal
structure that would otherwise remain hidden from observers. We will show that
this allows to measure with unprecedented precision the stellar masses and to
infer their envelope thicknesses, to probe the core chemical stratification,
and to detect rotation rates and magnetic fields. Consequently, in this work,
we also review the pulsational properties of white dwarfs and the most recent
applications of white dwarf asteroseismology.
