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In the recent years, the usage of private informations to make predictions and statistics, has grown significantly. This data, belonging both to smart objects and to classical computers, are commonly transferred to datacenters where Artificial Intelligence (AI) algorithm are applied in order to perform inference processes. The more are the data, and the more accurate are the models developed. However, some private informations cannot be shared: an example is depicted by the medical datasets where the medical exams, due to regulations on personal data protection cite {GDPR}, are protected and carefully stored. The Federated Learning (FL) approach, which is gaining more and more importance, aims to solve the privacy issue by exchanging only the parameters of the models and not the protected data. The final objective is always to exploit the information power of the private data in the nodes (called clients) to achieve a better common Machine Learning (ML) model. The aim of the thesis is to build and test the feasibility of a FL training process in the medical field. In the thesis, the analyzed inference task is the brain tumor segmentation through Magnetic Resonance Images (MRIs) coming from both public and private datasets. The thesis and the experiments were carried out in collaboration with Politecnico di Milano, Conseil européen pour la recherche nucléaire (CERN) and Consiglio Nazionale delle Ricerche (CNR) that, thanks to a non-disclosure agreement, permitted to obtain the private real dataset with anonymized data provided by the hospital of Athens (2nd Departement of Radiology) and a public dataset. The network architecture was …