Belmonte Beitia, Juan. 

The aim of the present review is to introduce the reader to some of the mathematical techniques that are relevant to the study of nonlinear Schr ̈odinger equation with inhomogeneous nonlinearity (i.e., the coefficients of the equation depends on the space). Upon introducing the general framework, we introduce some applications of this equation, as Bose-Einstein condensates. We then offer a collection of mathematical methods that can be used to understand the existence, orbital stability and to calculate analitical exact solutions of this equation.