Part 1 Invariant differentiation: vector fields, trajectories, invariants; lie differentiation in non-holonomic basis; the first appendixes. Part 2 Connection in the bundle: translation of fibres; linear connections, morphism of the bundles with the connections. Part 3 Ordinary differential equations: operator of total differentiation; lie fields and symmetries of equations; lighting of surfaces. Part 4 Partial differential equations: general constructions; characteristics of equations; Hamilton formalism. Part 5 Open problems: polynomial maps; iterations of the tangent functor; geometry of catastrophes.
