Analytic Combinatorics uses techniques from complex analysis to find estimates for the coefficients of generating functions.
It relates the discrete world of enumerative combinatorics to the continuous world of complex analysis.
It is associated with the work of Philippe Flajolet and Robert Sedgewick, although its techniques can be traced back to at least the early 20th century to people like Srinivasa Ramanujan and G. H. Hardy.
This book assumes you already have a reasonable understanding of generating functions. See w:Generating_function and v:Generating_functions.
It assumes little to no understanding of complex analysis. It should explain any complex analysis that you need to know.
The individual chapters will list their own prerequisites.