  The distance covariance of Sz\'ekely, et al. [23] and Sz\'ekely and Rizzo
[21], a powerful measure of dependence between sets of multivariate random
variables, has the crucial feature that it equals zero if and only if the sets
are mutually independent. Hence the distance covariance can be applied to
multivariate data to detect arbitrary types of non-linear associations between
sets of variables. We provide in this article a basic, albeit rigorous,
introductory treatment of the distance covariance. Our investigations yield an
approach that can be used as the foundation for presentation of this important
and timely topic even in advanced undergraduate- or junior graduate-level
courses on mathematical statistics.
