Abstract
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.
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