While not directly geared at the interest you mentioned, if a mathematician were trying to learn quantum gravity(perhaps to work in this field from the math side), I would recommend they consult the duo of books by Rovelli and Thiemann.

The first book focuses on the physics side, and builds your background in the physics of quantizing gravity from the loop quantum approach. The second book focuses on the mathematical methods used and the specific mathematical models currently in use. Additionally, both books provided me with much needed exposition in the field, feeding my desire as a mathematician to understand why many of these math structures apply to these physical phenomena.

The first book is Rovelli: Quantum Gravity, the second is Thiemann: Modern Canonical Quantum General Relativity.

I warn you they are large books.