Does anyone know of an "abstract algebra-esque" treatment of the extended complex plane and the Mobius transformations?
I am studying complex analysis now, and I am a little frustrated that my familiar algebraic environments have been replaced by apparently more esoteric and delicate structures.
(The book I am using is Ahflors, and I do think he does a good job of explaining the geometry and analysis of the situation. However, some of the connections to algebra, such as homogeneous coordinates, definitely feel a little mysterious to me...)