The course is focused on the use of geometric methods in problems of differential equations and physics. The study of symmetries and equivalence problems requires a number of tools and techniques, many of which have their origins in differential geometry. Therefore, our study of differential equations and variational problems will have essentially a geometric character, unlike analytical methods. We will start with differential manifolds and Lie groups, the method of the moving frames will be essential here. We will focus on both the globally geometric view and also on calculations in local coordinates. Special attention will be paid to nonlinear problems. We will also study calibration invariants in connection with Maxwell's equations and quantum field theory.