We introduce and use k-shell decomposition to investigate the topology of the Internet at the AS level. Our analysis separates the Internet into three sub-components: (a) a nucleus which is a small (~100 nodes) very well connected globally distributed subgraph; (b) a fractal sub-component that is able to connect the bulk of the Internet without congesting the nucleus, with self similar properties and critical exponents; and (c) dendrite-like structures, usually isolated nodes that are connected to the rest of the network through the nucleus only. This unique decomposition is robust, and provides insight into the underlying structure of the Internet and its functional consequences. Our approach is general and useful also when studying other complex networks.