The purpose of this book is to communicate some of the recent
advances in this field while preparing the reader for more advanced
study. The material can be roughly divided into three different
types: classical, standard but sometimes with a new twist, and
recent. The author first studies basic covering theorems and their
applications to analysis in metric measure spaces. This is followed
by a discussion on Sobolev spaces emphasizing principles that are
valid in larger contexts. The last few sections of the book present
a basic theory of quasisymmetric maps between metric spaces. Much
of the material is recent and appears for the first time in book
format.
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