The Kaluza-Klein idea: Status and prospects

The present status of the Kaluza-Klein idea is reviewed, including a discussion of the fermionic sector. Formalism and geometrical methods necessary for the formulation of high-dimensional field theories are described in some detail. The mechanism of spontaneous compactification is explained and a description of presently available models is given. A chapter on coset space reduction of high dimensional Yang-Mills theories is included. The review concludes with an outlook on supersymmetric models. (author)