After a brief introduction of general relativity for pedestrians is given venerable Hawking radiation is re-derived for a Schwarzschild black hole. It is found that the ground state of quantum black hole is described by a two-mode squeezed state of quantum optics! When a particle with spin is moving in the gravitational field, the descript of the spin requires the introduction, at each point, of an independent Lorentz coordinate frame, combined with the demand of invariance under local Lorentz transformation. The relation between local and general coordinates is conveyed by tetrads, family of vector fields. The Hilbert space vector for a spin ½ particle is also defined on the local inertial frame spanned by these tetrads, which is represented by generalized Wigner rotation. For more classical applications, an effective medium theory is presented, in which metric tensors, that represent the space-time curvature, is equivalently represented by the permittivity and the permeability tensors. In novel meta-materials such as an invisibility cloak is formulated based on the effective medium theory.