The aim of this book is to present short notes or articles, as well as studies on some topics of Geometry, Analysis, and Number Theory. The material is divided into ten chapters: * Geometry and geometric inequalities; * Sequences and series of real numbers; * Special numbers and sequences of integers; * Algebraic and analytic inequalities; * Euler gamma function; * Means and mean value theorems; * Functional equations and inequalities; * Diophantine equations; * Arithmetic functions; * Miscellaneous themes.