The studied theme in this monography is part of the geometric function theory domain. An important problem of the geometric theory of analytic functions is to study differential operators and their properties on different classes of analytic functions. A particular chapter in the differential operators study is to study the different geometric properties of some classes of analytic functions defined by these operators. The differential subordinations, superordinations, strong subordinations and strong superordinations have an important place in defining some new classes of holomorphic functions that are obtained using some generalizations of known differential operators. This monography presents the author'' research regarding the differential subordinations, superordinations, strong subordinations and strong superordinations using some differential operators, obtaining new subclasses of analytic functions. This monography is addressed to researchers and graduate students for research, seminars and advanced graduate courses in complex analysis.