• Introduction.- The Ernst Equation.- Riemann-Hilbert Problem and Fay's Identity.- Analyticity Properties and Limiting Cases.- Boundary Value Problems and Solutions.- Hyperelliptic Theta Functions and Spectral Methods.- Physical Properties.- Open Problems.- Riemann Surfaces and Theta Functions.- Ernst Equation and Twister Theory.- Index.

From the reviews: "This book covers these areas - the reduction of the Einstein vacuum equations to the Ernst equation, the reinterpretation of the Ernst equation as an integrable system and the use of techniques of integrable systems ... . This book provides an excellent exposition of these ideas; as well as providing a sound introduction ... . This is an excellently written monograph with an encyclopedic list of references and it should be of interest to a wide range of people ... ." (Ian A. B. Strachan, Mathematical Reviews, Issue 2006 k) "What the present book describes are some of the heroic efforts that have been undertaken to construct physically significant spacetimes by solving the vacuum Ernst equation. ... It is the reviewer's opinion that the resulting book will be more useful as a resource for those who are already well versed in the subject of integrable systems ... ." (Frederick J Ernst, Classical and Quantum Gravity, Vol. 24, 2007)