Abstract
Minimum log discrepancies are important for birational geometry. In this thesis, we first define jet schemes of a given scheme which is finite type over k. Then define space of arc by projective limit of jet schemes. Secondly, we discuss the relation between space of arcs and the birational transformation theorem. Finally, we give a new interpretation of minimum log discrepancies via space of arcs and we use this interpretation to prove a beautiful theorem-inversion of adjunction.