See at contact manifold for more.
Hansjörg Geiges, Contact geometry, in F.J.E. Dillen and L.C.A. Verstraelen, (eds.), Handbook of Differential Geometry vol. 2 North-Holland, Amsterdam (2006), pp. 315-382 (arXiv:math/0307242)
John Etnyre, Introductory lectures on contact geometry Proc. Sympos. Pure Math. 71 (2003), 81-107. (pdf)