REGULARIZED SEMIGROUPS AND NON-ELLIPTIC DIFFERENTIAL OPERATORS discusses the semi-group approach to non-elliptic differential operators, which was developed in the last two decades. A detailed introduction to the theory of regularized semigroups is provided. And then, the authors give the applications of regularized semigroups to non-elliptic differential operators with constant coefficients of time-dependent coefficients, parabolic systems, correct systems, abstract differential operators and pseudo differential operators. They also give the very recent use of regularized semigroups to Schrodinger operators.