These are the notes from the mini-course on Legendrian submanifolds and exact Lagrangian cobordisms given by the author at the Summer Workshop 2019 at Gokova Geometry-Topology Institute. In the mini-course we discuss classical invariants and modern invariants (coming from Chekanov-Eliashberg algebra) of Legendrian submanifolds in both low and high dimensions and the obstructions to the existence of exact Lagrangian cobordisms between Legendrian submanifolds coming from such Legendrian invariants. We do not claim originality of the material in these notes.