Tubes by Alfred Gray
This book expresses the full understanding of Weyl's formula for the volume of a tube, its roots and its implications. Historical notes and Mathematica drawings have been added to this revised second edition.
From the reviews:
Will do much to make Weyl's tube formula more accessible to modern readers.... A high point is the presentation of estimates for the volumes of tubes in ambient Riemannian manifolds whose curvature is bounded above or below.
--BULLETIN OF THE AMS