  We give a self-contained presentation of the basic results on jet schemes of
singular varieties. Applications are given to invariants of singularities, such
as minimal log discrepancies. We simplify our older approach to Inversion of
adjunction for locally complete intersection varieties, and we prove a more
general result for arbitrary Q-Gorenstein varieties embeded in nonsingular
varieties (this statement has been proved independently also by Kawakita) .
