This course is devoted to selected problems of classical (theoretical) and fluid mechanics which are usually remain outside the standard course of mechanics. Despite the fact that the course is aimed at students with an understanding of the methods and approaches of classical and fluid mechanics, several lectures of the course are devoted to revision of material from the course of classical (theoretical) mechanics. The course is aimed at an audience interested in theoretical physics methods for solving problems of classical and fluid mechanics. The course is designed for an audience that has previously attended general course of classical and fluid mechanics and courses of higher mathematics: mathematical analysis and differential equations theory.