Sheaves and symplectic geometry of cotangent bundles

This paper is essentially made of the three preprints arXiv:1212.5818,:1311.0187, arXiv:1603.07876 gathered in a single text, with simplified. We recall several results of the microlocal theory of sheaves of-Schapira and apply them to study the symplectic geometry of cotangent. We explain how we can recover the Gromov nonsqueezing theorem, the-Eliashberg rigidity theorem, the existence of graph selectors, we prove three cusps conjecture about curves on the sphere and we recover more recent on the topology of exact Lagrangian submanifolds of cotangent bundles.