Designing Machine Learning algorithms implies to answer three main questions: First, what is the space H of hypotheses or models of the data that the algorithm considers? Second, what is the inductive criterion used to assess the merit of a hypothesis given the data? Third, given the space H and the inductive criterion, how is the exploration of H carried on in order to find a as good as possible hypothesis? Any learning algorithm can be analyzed along these three questions. This chapter focusses primarily on unsupervised learning, on one hand, and supervised learning, on the other hand. For each, the foremost problems are described as well as the main existing approaches. In particular, the interplay between the structure that can be endowed over the hypothesis space and the optimisation techniques that can in consequence be used is underlined. We cover especially the major existing methods for clustering: prototype-based, generative-based, density-based, spectral based, hierarchical, and conceptual and visit the validation techniques available. For supervised learning, the generative and discriminative approaches are contrasted and a wide variety of linear methods in which we include the Support Vector Machines and Boosting are presented. Multi-Layer neural networks and deep learning methods are discussed. Some additional methods are illustrated, and we describe other learning problems including semi-supervised learning, active learning, online learning, transfer learning, learning to rank, learning recommendations, and identifying causal relationships. We conclude this survey by suggesting new directions for research.