  In this lecture a short introduction is given into the theory of the Feynman
path integral in quantum mechanics. The general formulation in Riemann spaces
will be given based on the Weyl- ordering prescription, respectively product
ordering prescription, in the quantum Hamiltonian. Also, the theory of
space-time transformations and separation of variables will be outlined. As
elementary examples I discuss the usual harmonic oscillator, the radial
harmonic oscillator, and the Coulomb potential. Lecture given at the graduate
college ''Quantenfeldtheorie und deren Anwendung in der Elementarteilchen- und
Festk\"orperphysik'', Universit\"at Leipzig, 16-26 November 1992.
