Lickorish and Wallace proved that any closed orientable connected 3-manifold can be obtained by integral Dehn surgery on a framed link in the 3-sphere.
Kirby calculus is a modifying method of surgery diagram of a 3-manifold by using some moves called Kirby moves.
This surgery diagram corresponds to a 4-dimensional handlebody(4-manifolds with boundary).
In this talk, I will explain this correspondence and give some applications.