Today data analysis is a key element of decision making in nearly all human affairs including industry, management, social policy and many others. Most methods of Data Analysis have a mathematical background. This equally applies to traditional statistical methods and to more recently developed methods of Data Analysis such as the Topological Data Analysis. The aim of the present course is to introduce students to a minimal mathematical core of today’s Data Analysis and show how it is used in practice via a number of simple examples. It comprises foundations of Probability theory, elements of Linear Algebra and theory of Metric spaces, Graph theory and, finally, some basic Combinatorial Topology. Throughout the course these and some other mathematical concepts and mathematical theories are accompanied with examples of their use in practice.