The numerous results of the searches for Dark Matter (DM) can be used to constrain the parameter space of many Beyond the Standard Model (BSM) theories. The focus on this Studentship was the development of the new features of MadDM, and the release of version 3.0  a plugin of the MadGraph5_aMC@NLO framework. The most important feature of MadDM 3.0 is a dedicated module for the calculation of the theory predictions for DM annihilation, as well as the comparison with the latest results from the Fermi-LAT experiment for DM annihilation into gamma rays in dwarf spheroidal galaxies. This new module extends the capabilities of the previous versions, i.e. the computation of the relic density and the direct detection rates, making MadDM 3.0 a comprehensive tool for the study of Dark Matter phenomenology.   With its user friendly interface, MadDM 3.0 allows the users to choose between two running modes. The precision' mode is based on the full chain of Monte Carlo sample production and Fermi-LAT limits calculation, and can be used for any generic model and DM annihilation into any generic final state. The fast' running mode can be used only for 2 body annihilation into Standard Model channels, and the limits are extracted from the dedicated module of experimental results; despite being less general, it can be efficiently used to scan and test large parameter spaces. The new version 3.0 was released in March 2018 together with its extended user manual (arXiv:1804.00044) which was recently accepted for publication in Physics of the Dark Universe.