This text was written for advanced undergraduate and beginners graduated students, as well as researchers who want to deepen their knowledge in some mathematical methods very useful in the recent economic literature (ordinary difference and differential equations, static and dynamic optimizations). It has been made through the experience of lecturing conducted teaching for many years in advanced courses in Mathematics for Economists at the University of Cagliari, Department of Economics and Business Science. The didactic format aims to present the necessary theory recalls at the beginning of each chapter and then proposes a series of exercises carried out, discussed, problems and deepening of some topics through a lot of economic applications. So the text follows the style of the lectures. It starts with some preliminary topics (geometry, algebra and mathematical analysis) and then it deals with ordinary difference and differential equations and some tools for static and dynamic optimization of functions of one and several variables. The readers have the chance to strengthen and deepen their preparation in the mathematical topics, through the exercises and problems proposed.