My research mainly focuses on learning theory, data science, and approximation theory. Analyzing and processing data has been an important task in various fields of science and technology, for which machine learning produces efficient algorithms. Learning theory studies the mathematical foundations of machine learning and helps design new algorithms. Starting from the work on statistical learning theory and support vector machines, it has been developed very fast and raised many challenging tasks and related theoretical issues concerning huge data of large variables: clustering, ranking, feature selection, dimension reduction, sparsity, and deep learning. I investigate the topics in learning theory and related machine learning algorithms using fundamental tools provided by probability analysis, statistics, optimization, and approximation theory.