  This article consisted of an elementary introduction to deformation theory of
varieties, schemes and manifolds, with some applications to local and global
shtukas and fever to Newton polygons of $p$-divisible groups . Soft problems
and results mainly are considered. In the framework we give review of some
novel results in the theory of local shtukas, Anderson-modules, global shtukas,
Newton polygons of $p$-divisible groups and on deformations of $p$-divisible
groups with given Newton polygons.
