I describe a brief summary of quantum mechanics and principles of scanning tunneling microscopy (STM) in this chapter. Quantum tunneling is an important concept to describe the transportation of small particles, like electron and hydrogen. In Sect. 2.1 I focus on H-atom tunneling in a double minimum potential that is the simplest but a ubiquitous system in physics and chemistry. Quantum tunneling of electron directly relates to the principle of the STM. In Sect. 2.2 the principles and applications of STM are described. I focus on the inelastic electron tunneling process in an STM junction, which can be applied to the vibration spectroscopy and reaction control of single molecules.