Differential Geometry is often considered as a "classical"
field in Mathematics. Yet it has recently been the object
of a substantial renewed interest, thanks in particular
to various applications where it plays an essential role.
After a quick review of some basic notions of Differential
Geometry, such as the fundamental forms of a surface or
the fundamental theorem of surface theory, some applications
- old and new - will be likewise briefly reviewed, such
as cartography, the theory of elastic shells, or the optimization
of the shape of gears.
This lecture is intended for undergraduate and graduate
students. No a priori knowledge of Differential Geometry
will be assumed.