Foundational textbook(s) for Complexity and Computability on Real Numbers
There are some good books - 
 1. Computable Analysis - Pour-El and Richards (an older reference)
 2. Computable Analysis - Weihrauch 

There's also the Blum-Shub-Smale Model, which is the model explored in "Complexity and Real Computation".

The complexity theory of computability of reals is explored in 
 1. Computational Complexity of real functions  - Ker-I Ko

A regular conference which explores this area is "Computability and Complexity in Analysis", held annually.