This book highlights the latest developments in the geometry of measurable sets presenting
them in simple straightforward terms. It addresses nonlocal notions of perimeter and curvature
and studies in detail the minimal surfaces associated with them. These notions of nonlocal
perimeter and curvature are defined on the basis of a non-singular kernel. Further when the
kernel is appropriately rescaled they converge toward the classical perimeter and curvature as
the rescaling parameter tends to zero. In this way the usual notions can be recovered by using
the nonlocal ones. In addition nonlocal heat content is studied and an asymptotic expansion is
obtained. Given its scope the book is intended for undergraduate and graduate students as
well as senior researchers interested in analysis and or geometry.
