  In this revised version, the mistake of the author confusing the weak
transform and strict transform, pointed out by E. Bierstone, is corrected. It
gives a self-contained proof of (embedded) resolution of singularities over a
field of characteristic zero following the inductive algorithm of Encinas and
Villamayor. A chapter explaining the background motivation for the invariants
used (based upon a lecture by Villamayor) and another containing some examples
demonstrating the subtle points are added.
