Abstract: After a brief general introduction into the basic principles of
asteroseismology, we consider the various restoring forces and the
approximations adopted in the theory of stellar oscillations.  We
discuss the corresponding waves and frequency regimes encountered in
modern space photometric light curves of various types of nonradial
pulsators across the Hertzsprung-Russell diagram.  Building on
well-established asteroseismic studies of slowly rotating stars, we
dive deep into moderate and fast rotators. We highlight some of their
internal properties treating individual pulsators, galactic
populations, and young open clusters. We end with an outlook towards
future observational and theoretical progress in asteroseismic probing
of stellar interiors.