This course aims at introducing basic concepts of probability and statistics useful in a great extend in several other courses. The course assumes that everybody has some basic idea about statistics, so the focus will be given to clarify the usefulness and the importance of the approaches and how Statistics can considerably help the decision making process. To this direction a brief introduction to basic principles of probability theory will be given and their connection to problems in Statistics. Basic statistical ideas for descriptive statistics and data visualization will be discussed together with problems of statistical inference like estimation and hypothesis testing. Regression type models will be discussed, including simple, multiple, logistic regression and a brief introduction to generalized linear models. Issues of statistical processing control will be provided. The Bayesian approach in statistical modeling offering certain possibilities with huge datasets will be introduced and worked. All material will be focused mainly on applications but the basic statistical insight will be discussed in depth. Also focus on problems and their modern solutions with big data will be discussed.