Enumeration of Rational Curves Via Torus Actions

I will explain some of the ideas from Kontsevich's paper with the same title. We will express the count of rational nodal curves of degree d on P^2 passing through 3d-1 points as some integral on the moduli space of stable maps to P^2. The torus action on P^2 will lift to this space and we will compute the integral using Bott's localization formula for equivariant integrals. In order to do this I will talk about how to compute the tangent space of the moduli space of stable maps at some points and figure out what the action of the torus should be on them by working as examples the degree 1 and 2 case.