  The utilization of statistical methods an their applications within the new
field of study known as Topological Data Analysis has has tremendous potential
for broadening our exploration and understanding of complex, high-dimensional
data spaces. This paper provides an introductory overview of the mathematical
underpinnings of Topological Data Analysis, the workflow to convert samples of
data to topological summary statistics, and some of the statistical methods
developed for performing inference on these topological summary statistics. The
intention of this non-technical overview is to motivate statisticians who are
interested in learning more about the subject.
