The study of deformations of algebro-geometric structures provides information about the local behaviour of the moduli space of those structures. In particular, we are interested in understanding how singular our moduli space can be at a fixed point. This amounts to the study of so-called obstructions for the related deformation functor.
I will show an algebraic approach to studying deformation problems which is especially useful for computing these obstructions. Finally I will discuss some examples.