  After a short biographical summary of the scientific life of Oskar Klein, a
more detailed and hopefully didactic presentation of his derivation of the
relativistic Klein-Gordon wave equation is given. It was a result coming out of
his unification of electromagnetism and gravitation based on Einstein's general
theory of relativity in a five-dimensional spacetime. This idea had previously
been explored by Kaluza, but Klein made it more acceptable by suggesting that
the extra dimension could be compactified and therefore remain unobservable
when it is small enough.
