This report comprises the first contributions from different partners on Federated Learning (FL). After a preliminary introductory section where the fundamental procedures and limitations are described, we detail the well-known mathematical foundation of Federated Learning for convex problems. In this case, we present a key algorithm, Alternating Direction Multipliers Method (ADMM), which is able to implement in a distributed way some fundamental problems such as regression (Ridge and LASSO) and classification (Logistic Regression and Support Vector Machines (SVM)). This procedure shares the fundamental approach of FL, which consists of performing some local processing, sharing some intermediate information and updating the local information with some global innovation. In a second step we introduce the extension of this approach to non-convex problems using Bayesian Neural Networks (BNN) where the update is based on the cooperative construction of the posterior of weights from different architectures. Several sections follow where different partners provide different contributions describing our first initiatives on the topic. Some preliminary code from all partners has been uploaded to a common repository to start creating a pool of methods and tools to foster incoming synergies.