Prem K. Kythe 
Handbook of Conformal Mappings and Applications [PDF ebook] 

The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem – for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk. The Handbook of Conformal Mappings and Applications is a compendium of at least all known conformal maps to date, with diagrams and description, and all possible applications in different scientific disciplines, such as: fluid flows, heat transfer, acoustics, electromagnetic fields as static fields in electricity and magnetism, various mathematical models and methods, including solutions of certain integral equations.