Topological insulators and topological superconductors are new kinds of materials with gapped states in bulk and gapless states in boundary. These gapless boundary states are robust due to the nontrivial topology. The spin/pesudospin of the boundary states form spin texture in real space, and in-gap transportation is also induced by the boundary states. Such properties can be used to construct spintronic devices, offering potentially dramatic benefits in the semiconductor industries. This book first gives a brief introduction to topological materials, and discusses the typical Hamiltonians of topological insulators and topological superconductors, with a focus on group IV materials.