Looking at my bookshelf, there's a few other books that come to mind:

Ahlfors & Sario. Riemann Surfaces.

Jost. Compact Riemann Surfaces.

Maskit. Kleinian Groups.

Tromba. Teichmuller theory in Riemannian geometry.

Farkas and Kra. Riemann Surfaces.

For my own purposes the Hubbard book is what I'd consider a natural starting point.

Looking at my bookshelf, there's a few other books that come to mind with varying levels of relevance:

Ahlfors & Sario. Riemann Surfaces.

Jost. Compact Riemann Surfaces.

Maskit. Kleinian Groups.

Tromba. Teichmuller theory in Riemannian geometry.

Farkas and Kra. Riemann Surfaces.

For my own purposes the Hubbard book is what I'd consider a natural starting point.