In this talk, we present a pathwise approach to stochastic
integration: Using the concepts of quadratic variation and Lévy area of
a continuous path along a sequence of time partitions, we construct a
pathwise integral as a limit of general Riemann sums. In a probabilistic
framework, when the underlying process is a semimartingale, this notion
of integration is consistent with stochastic integration. Furthermore,
we state necessary and sufficient conditions for the quadratic variation
and Lévy area of a continuous path to be invariant with respect to the
choice of the partition sequence.