  This is an introduction to Wiener measure and the Feynman-Kac formula on
general Riemannian manifolds for Riemannian geometers with little or no
background in stochastics. We explain the construction of Wiener measure based
on the heat kernel in full detail and we prove the Feynman-Kac formula for
Schr\"odinger operators with $L^\infty$-potentials. We also consider normal
Riemannian coverings and show that projecting and lifting of paths are inverse
operations which respect the Wiener measure.
