Asymptotic Theory of Finite Dimensional Normed Spaces: Isoperimetric Inequalities in Riemannian Manifolds (Lecture Notes in Mathematics, 1200)

I would suggest that anyone interested in "asymptotic geometry" start with this short book, which is written with love by two of the people who created the field (the results of which are not only interesting in and of themselves, but are used in many other areas). Yes, the price is outrageous (for a mimeographed paperback), but that's why God created libraries.