Arc spaces, motivic integration and stringy invariants
  We provide a gentle introduction to arc spaces, motivic integration and stringy invariants. We explain the basic concepts and first results, including the p-adic number theoretic pre-history, and we provide concrete examples.   The text is a slightly adapted version of the 'extended abstract' of the author's talks at the 12th MSJ-IRI "Singularity Theory and Its Applications" (2003) in Sapporo. At the end we included a list of various recent results. 
Willem Veys