  Impurities are ubiquitous in condensed matter. Boundary Conformal Field
Theory (BCFT) provides a powerful method to study a localized quantum impurity
interacting with a gapless continuum of excitations. The results can also be
implied to nanoscopic devices like quantum dots. In these lecture notes, I
review this field, including the following topics: I. General Renormalization
Group (RG) framework for quantum impurity problems: example of simplest Kondo
model II. Multi-channel Kondo model III. Quantum Dots: experimental
realizations of one and two channel Kondo models IV. Impurities in Luttinger
liquids: point contact in a quantum wire V. Quantum impurity entanglement
entropy VI. Y-junctions of Luttinger liquids VII. Boundary condition changing
operators and the X-ray edge problem.
