The course aims to provide a solid presentation of the main approaches to statistical inference, in particular of those formulations based on the so-called likelihood function, and of the most important statistical methods in current use for data modeling and for the interpretation of the uncertainty inherent in the conclusions from statistical analyses. The course is intended for students in science, engineering and statistics. At the end of the course, the student should be able to select and apply the main statistical procedures to a wide range of practical problems.