Crystalline comparison theorem for p-divisible groups

Let $p$ be a prime number and $K$ a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p$. The aim of the master thesis is to understand Messing's crystalline Dieudonné theory and deformation theory of $p$-divisible groups, in order to prove the classification of $p$-divisible groups over the ring of integers of $K$ with Breuil-Kisin modules. Using crystalline techniques, this allows to relate the $p$-adic Tate module of a $p$-divisible group and its Breuil-Kisin module by a period isomorphism, which in this case is nothing but the crystalline comparison isomorphism between the dual of the étale cohomology and that of the crystalline cohomology of the special fiber.