Finding a relation between singularities of a variety and singularities of subvarietes is a natural problem. An answer to the problem, called adjunction and inversion of adjunction for log canonical pairs, plays a critical role in the recent developments of the birational geometry. In this talk, I will introduce a generalization of the result, that is, adjunction and inversion of adjunction for normal pairs. This is a joint work with Osamu Fujino.