Abstract: In the last decade, the number of exoplanets discovered has grown exponentially, mainly due to Kepler observations which, along with observations of the K2 mission, announced the discovery of 1284 planets at once in 2016. These discoveries were done using the planetary transit method, which has low sensitivity for low-mass planets far away from their stars. Thus most of the discoveries of giant planets were of orbits close to their stars. In contrast, the gravitational microlensing technique is sensitive to low-mass planets orbiting between $ 0.5 $ AU and $ 10 $ $ AU $. Because it depends only on the combined gravitational field of the star-planet, this technique can detect planets around low brightness stars, which would be difficult for other techniques that depend on star emitted light. Until now, astronomers have discovered 47 planets through this technique, which is relatively low number, when compared to the other methods like transit and radial velocity. In this dissertation we show in detail the equations behind the gravitational microlensing theory and its applications to detect distant low-mass planets. We focus on the characterization of systems with closed topology, where the planet has between 10^-5 and10^-6 of the mass of the star and with a semi-major axis about 1 AU (planet with Earth-like mass around 1AU of a star with Sun-like mass). We also present a suggestion of parameterization for the impact parameter \mu_0 and the impact angle \alpha in order to reduce the search time consuming for light curves generated from systems with close topology. We present the main steps for the development of two algorithms that use the semi-analytical method of solution of the lens equation and the brute force of simulation method Inverse Ray Shooting (IRS) respectively. These codes simulate the topology and light curve of microlensing events, and were used to simulate our systems presented in this dissertation. As a main result, we demonstrate the ability of the model to generate theoretical curves and compared these light curves with real microlensing events.