The variation problem for mechanics is exposed in this chapter. This means the searching for stationary points (extremals) of a certain variational functional (a map assigning to sections of the given fibred manifold values of the certain integral from a specific horizontal differential form—Lagrangian). The concrete Lagrangian is determined by the problem being solved, mathematical (e.g. finding the shortest line connecting two points on a sphere) or physical (finding the trajectory of a physical system). Extremals are finally searched as sections leading to zero value of so called variational derivative of the primary variational functional, expressed as the variational integral from the Lie derivative of the initial Lagrangian \(\lambda \) . The famous first variational formula in both the integral and infinitesimal form is derived. The Lepage equivalent \(\theta _\lambda \) of a Lagrangian (well-known Cartan form) is introduced, the Euler-Lagrange form \(E_\lambda \) is directly derived from it. Extremals are then found as sections along which the Euler-Lagrange form vanishes, i.e. the solutions of Euler-Lagrange equations well-known from the classical calculus of variations. Symmetries of a Lagrangian are defined and corresponding conservation laws are obtained (Noether theorem, Noether equation, Noether currents). Symmetries of the Euler-Lagrange form then give the Noether-Bessel-Hagen equation.