Evolutionary and pulsational properties of white dwarf stars

White dwarf stars are the final evolutionary stage of the vast majority of stars, including our Sun. Since the coolest white dwarfs are very old objects, the present population of white dwarfs contains a wealth of information on the evolution of stars from birth to death, and on the star formation rate throughout the history of our Galaxy. Thus, the study of white dwarfs has potential applications in different fields of astrophysics. In particular, white dwarfs 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, such as our Galaxy and open and globular clusters. In addition, the high densities and temperatures characterizing white dwarfs allow these stars to be used as cosmic laboratories for studying physical processes under extreme conditions that cannot be achieved in terrestrial laboratories. Last but not least, since many white dwarf stars undergo pulsational instabilities, the study of their properties constitutes a powerful tool for applications beyond stellar astrophysics. In particular, white dwarfs 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. These potential applications of white dwarfs have led to renewed interest in the calculation of very detailed evolutionary and pulsational models for these stars. In this work, we review the essentials of the physics of white dwarf stars. We enumerate the reasons that make these stars excellent chronometers, and we describe why white dwarfs provide tools for a wide variety of applications. 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 a unique opportunity to peer into their internal structure that would otherwise remain hidden from observers. We will show that this allows one to measure stellar masses with unprecedented precision 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.