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The aim of this monograph is to present our recent progresses on the periodic stabilization for some linear and time-periodic evolution equations which contains both finite and infinite dimensional systems. These progresses may lead us to com-prehensive understanding of the subject on the periodic stabilization. Several criteria on the periodic feedback stabilization for linear periodic controlled systems are given from perspective of algebra, geometry and analysis. This monograph summarizes our ideas, results and methods on this subject in recent years. We tried our best to make the material self-contained as far as possible.