  The objective of this introduction to Colombeau algebras of
generalized-functions (in which distributions can be freely multiplied) is to
explain in elementary terms the essential concepts necessary for their
application to basic non-linear problems in classical physics.
  Examples are given in hydrodynamics and electrodynamics. The problem of the
self-energy of a point electric charge is worked out in detail: The Coulomb
potential and field are defined as Colombeau generalized-functions, and
integrals of nonlinear expressions corresponding to products of distributions
(such as the square of the Coulomb field and the square of the delta-function)
are calculated.
  Finally, the methods introduced in Eur. J. Phys. /28/ (2007) 267-275,
1021-1042, and 1241, to deal with point-like singularities in classical
electrodynamics are confirmed.
