Dmitry Fuchs (Univ. of California, Davis) KNOTS IN CONTACT GEOMETRY Legendrian knots in the standard contact space are smooth knots in space tangent to the plane distribution determined by the form y dx - dz. There are classical (the Thurston-Bennequin and rotation numbers) and more modern (contact homology) Legendrian isotopy invariants of Legendrian knots. A (generic) Legendrian knot is determined by its xz-projection (aka the front projection) which is a smooth closed curve in the plane with transverse self-intersections and cusps but without vertical tangents and self-tangencies. In the early 2000's, a visualizable combinatorial structure on front diagram was discovered (independently, by Chekanov, Pushkar, and the speaker); it is called a normal ruling. The existence of a normal ruling turns out to be necessary and sufficient for some seemingly unrelated properties of Legendrian knots, such as the existence of a generating family of functions and certain relations between the abovementioned invariants. The talk will contain a survey of results of this kind with an emphasis on a recently discovered connections between the generating families and the contact homology.