The results contained in the book are related to the field of Complex Analysis of one complex variable. The classical notions of differential subordination and its dual, differential superordination, introduced by S.S.Miller and P.T.Mocanu are the starting point for new differential subordinations and superordinations obtained using differential and integral operators and the classical methods of the admissible functions theory. Using the notion of strong differential subordination introduced by J.A.Antonino and S.Romaguera, the author introduced in a published paper the dual notion of strong differential superordination. As a novelty, the book shows in two chapters the results of a joint work with Professor Gheorghe Oros in extending the classical theory of differential subordination and superordination to those new notions. Also, a new approach given by the author to the study of strong differential subordination and strong differential superordination by introducing some special classes of functions can be seen.The book can be useful to researchers who study for their PhD and to all researchers whose activity is oriented twards the domain of Geometric Function Theory.