The theory of deformations goes back to Riemann, who studied the deformation

parameters for Riemann surfaces in 1857. A century later, Kodaira and Spencer

developed the idea of deformations of complex manifolds. Cohomology theory

is strongly related to deformations.

In this talk, I will give a brief survey of deformation theory.

The deformation cohomology for Lie algebroids will be discussed,

as well as some applications in Poisson geometry.