The topic of this paper is strongly convex functions. The paper is divided into five chapters. The first chapter contains basic concepts and theorems that we use in paper. The definition, examples and description of basic properties of convex functions are given, and then the operations with convex functions are described. At the end of the first chapter there is a connection of convex functions with Jensen’s inequality and the Hermite-Hadamard inequality, which is also the characterization of convex functions. In the second chapter, we introduce the notion of strongly convex functions as a generalization of convex functions. Definition of convex function is: Let \(I\subset\mathbb{}{R}\) be an interval and \(c\) be a positive number. A function \(f:I \rightarrow \mathbb{R}\) is called strongly convex function with modulus \(c\) if \( f(\lambda x+(1-\lambda)y)\leq \lambda f(x)+(1-\lambda)f(y)-c\lambda(1-\lambda)(x-y)^2,\), for all \(x,y \in I\) and \(\lambda\in [0,1] \). Also, in the second chapter, some properties of convex functions are generalized for strongly convex functions. In the third chapter, we state and prove the generalization of the Jensen and Hermite-Hadamard inequalities for strongly convex functions and several theorems related to the Hermite-Hadamard inequality. The fourth chapter provides an insight into the characterization of the unitary space using strongly convex functions. In the fifth chapter, we give a generalization of the separation theorem for strongly convex functions.