The study of tight contact structures on closed 3-manifolds turned out
to be a very effective way for understanding certain geometric
properties of the 3-manifold at hand. In the lecture we show a way to
find such structures and prove their tightness in some particular cases.
For example, we show that the result of almost any rational surgery on a
positive torus knot admits a tight contact structure. Tightness will be
proved by applying contact invariants recently introduced by Ozsvath and
Szabo.