This mini-course will introduce a renormalization operator for dissipative Henon-like maps. The fixed point of the one-dimensional renormalization operator will also be a hyperbolic fixed point of the Henon-renormalization operator. This corresponds to universal geometrical properties of the Cantor attractor of infinitely renormalizable Henon-like maps. However, the two-dimensional theory is richer than the unimodal case. In particular, the Cantor attractor is not rigid, does not lie on a smooth curve and generically does not have bounded geometry. The quantitative aspects of these phenomena are controlled by the average Jacobian.

The global topological properties of finitely renormalizable Henon-like maps in phase and parameter space are also controlled by the average Jacobian. In particular, density of hyperbolicity will be discussed in a neighborhood of the infinitely renormalizable maps.