  We present a concise proof for the existence and construction of a {\it
strong resolution of excellent schemes} of finite type over a field of
characteristic zero. Our proof is based on earlier work of Villamayor,
Encinas-Villamayor and Bierstone-Milman. It apports some substantial
simplifications which may be helpful for a better understanding of how to prove
Hironaka's famous theorem.
