The increasing volume and nature of big data sets in business, economics, social and political sciences call for more complex and sophisticated mathematical and data mining tools. The complex systems monitored by big data bases are successfully described in terms of networks. In this course we will present and discuss mathematical and data mining tools used to characterize large empirical or model networks. Large data sets will be computationally investigated and the limits of the used algorithms will be discussed. The assessment of the statistical validity of the observed results will be analyzed and, when possible, quantitatively evaluated. Besides the mathematical theory, the course will have a practical approach with homeworks, hands-on classes and with the development of a project. During the class all examples and sample codes will be provided in Python and Jupyter notebooks.