I am interested in learning Teichmuller theory. Previously, I learnt 2 dimensional hyperbolic geometry from S. Katok's book. Now, I am interested in learning about significance of hyperbolic geometry in low dimensional geometry, i.e. Hyperbolic surfaces and their Teichmuller spaces. But I found that to learn Teichmuller theory one should learn some 3- dimensional hyperbolic geometry first. I want to know about what is 3- dimensional hyperbolic geometry.
How should I learn it (3- dimensional hyperbolic geometry)? Which books/ papers I should follow? Is the subject connected to Teichmuller theory?