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Stellar pulsations provide a complex system in stars. This complexity is studied by analyzing the non-sinusoidal, semi-regular, or irregular light curves. This unique volume summarizes the application of recent theoretical results obtained from stellar pulsation studies. In addition, the latest developments in hydrodynamic simulations are discussed. A historical sketch of the study of beat Cepheids, first known for their variable amplitudes, is given as an introduction to the book. This introduction clearly demonstrates how complicated the study of variable stars can be, and therefore challenges and invites the reader to study the entire book.