Dedicated to the memory of Wolfgang Classical Intersection Theory (see for example Wei Wei]) treats the case of proper intersections, where geometrical objects (usually subvarieties of a non- singular variety) intersect with the expected dimension. In 1984, two books appeared which surveyed and developed work by the individual authors, co- workers and others on a refined version of Intersection Theory, treating the case of possibly improper intersections, where the intersection could have ex- cess dimension. The first, by W. Fulton Full] (recently revised in updated form), used a...