In sufficiently complete textbooks on theoretical mechanics for technical universities, analytical mechanics is given due attention. However, there are no sections of theoretical mechanics that are important for modern applied problems. So, traditionally non-holonomic systems are not considered, which include many technical devices. The same applies to the integral, variational principles of mechanics.. The present manual outlines the basics of analytical mechanics of both holonomic and non-holonomic systems . Differential and some integral variational principles of mechanics and their applications are considered Summary of necessary information from the variational calculus. The manual will be useful for undergraduate and graduate students, as well as engineers using the methods of analytical mechanics in the study of the movements of complex systems.