What is big data? What the students can imagine? In this lecture, the term big data as well as the practical examples of big data will be presented. We will show how the big data is processed by computers and why we analyse it. In present, people use the social networks, Internet provides important information about the exchange rates, hospitals keep the information about their patients etc. Information is everywhere. When we process a huge amount of information, we can find out, for example, some patterns in behaviour of patients with the lung cancer, predict some trends in the exchange rates or to identify interactions between special communities on Facebook. To process such amount of information, it is necessary to use the modern approaches. Mathematical science is considered to be a stepping stone in this area of research.