In this book we report on the semigroup approach to non-elliptic differential opera- tors. which was developed in the last two decades. A detailed introduction to the theory of regularized semigroups is provided. And then we give the applications of regularized semigroups to non-elliptic differential operators with constant coeffi-cients or time-dependent coefficients， parabolic systems， correct systems， abstract differential operators and pseudo differential operators. We also give the very recent use of regularized semigroups to Schrodinger operators.