Recently I am reading the book Low Dimensional Geometry, From Euclidean Surface to Hyperbolic Knots by the author Francis Bonahon . In this book in chapter 7, define notion of group of transformation, basically a group acts on a metric space and the quotient space again a metric (for details kindly go through the book, page 185). To view of this notion I have some curiosity that, In Riemannian Geometry, Riemannian manifolds are basically are metric spaces(with respect to Riemannian metric), I have read very basic of Riemannian Geometry, any one can see please refer me some good book where I can study Riemannian Geometry via metric spaces and group of isometries.
Thanks