Maybe this great book
[Comparison Theorems in Riemannian Geometry][1] by Jeff Cheeger and David Ebin. For seeing greatness read the reviews of this book:

> - ... this is a wonderful book, full of fundamental techniques and ideas. (Robert L. Bryant)
- Cheeger and Ebin's book is a truly important classic monograph in Riemannian geometry, with great continuing relevance. (Rafe Mazzeo)

  [1]: https://bookstore.ams.org/chel-365-h