  We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of
the renormalization transformation of bounded type. This gives the first
computer-free proof of the original Feigenbaum observation of the universal
parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor's
conjectures on self-similarity and "hairiness" of the Mandelbrot set near the
corresponding parameter values. We also conclude that the set of real
infinitely renormalizable quadratics of type bounded by some N>1 has Hausdorff
dimension strictly between 0 and 1. In the course of getting these results we
supply the space of quadratic-like germs with a complex analytic structure and
demonstrate that the hybrid classes form a complex codimension-one foliation of
the connectedness locus.
