The recent research domain of asteroseismology studies the internal structure of stars, which is not directly observable, through the interpretation of the frequency spectra of stellar oscillations. The basic principles of asteroseismology are very similar to those developed by earth seismologists. Stellar interiors can be probed from oscillations because different oscillation modes penetrate to different depths inside the star. Asteroseismology is the only available method to derive the internal structure of the stars with high precision. This book - the first on asteroseismology - offers a practical guide for graduate students and scientists working in stellar astrophysics. It provides a general introduction to asteroseismology, and comprehensive coverage of all its aspects: fundamental theory, observations and observational techniques, methodology of data analysis, and seismic interpretations of various classes of multi-periodic pulsating stars.