  This is a gentle introduction to Colombeau nonlinear generalized functions, a
generalization of the concept of distributions such that distributions can
freely be multiplied. It is intended to physicists and applied mathematicians
who prefer a `step-by-step approach' to a `top-down indoctrination.'
  No particular prerequisite knowledge is necessary -- and in less than one
hour you should know everything you need to know and were afraid to ask about
Colombeau algebras and their applications in physics...
  A selected bibliography is appended, giving examples of applications to
partial differential and wave equations, electrodynamics, hydrodynamics,
general relativity, and quantum field theory.
