The Geometry of Jet Multi-time Lagrange and Hamilton Spaces

We begin with a lapidary presentation of the mathematical and physical context in which these geometries are placed. From this point of view, we will point out both the similarities and the differences between our geometries and the geometrical theories developed during the last years - these geometrical theories are constructed starting from ordinary Lagrangians and Hamiltonians or multi-time Lagrangians and Hamiltonians of first order.

At the same time, we will try in this introduction to briefly emphasize the main elements which offer our multi-time Lagrange-Hamilton geometrical theory a new character and some notes of originality.