From the reviews: "This book provides a detailed exposition of Thomae's formula for cyclic covers of CP1, in the non-singular case and in the singular case for Zn curves of a particular shape. ... This book is written for graduate students as well as young researchers ... . In any case, the reader should be acquainted with complex analysis (in several variables), Riemann surfaces, and some elementary algebraic geometry. It is a very readable book. The theory is always illustrated with examples in a very generous mathematical style." (Juan M. Cervino Mathematical Reviews, Issue 2012 f) "In the book under review, the authors present the background necessary to understand and then prove Thomae's formula for Zn curves. ... The point of view of the book is to work out Thomae formulae for Zn curves from 'first principles', i.e. just using Riemann's theory of theta functions. ... the 'elementary' approach which is chosen in the book makes it a nice development of Riemann's ideas and accessible to graduate students and young researchers." (Christophe Ritzenthaler, Zentralblatt MATH, Vol. 1222, 2011)

• - Introduction.- 1. Riemann Surfaces.- 2. Zn Curves.- 3. Examples of Thomae Formulae.- 4. Thomae Formulae for Nonsingular Zn Curves.- 5. Thomae Formulae for Singular Zn Curves.-6. Some More Singular Zn Curves.-Appendix A. Constructions and Generalizations for the Nonsingular and Singular Cases.-Appendix B. The Construction and Basepoint Change Formulae for the Symmetric Equation Case.-References.-List of Symbols.-Index.

From the reviews: "This book provides a detailed exposition of Thomae's formula for cyclic covers of CP1, in the non-singular case and in the singular case for Zn curves of a particular shape. ... This book is written for graduate students as well as young researchers ... . In any case, the reader should be acquainted with complex analysis (in several variables), Riemann surfaces, and some elementary algebraic geometry. It is a very readable book. The theory is always illustrated with examples in a very generous mathematical style." (Juan M. Cervino Mathematical Reviews, Issue 2012 f) "In the book under review, the authors present the background necessary to understand and then prove Thomae's formula for Zn curves. ... The point of view of the book is to work out Thomae formulae for Zn curves from 'first principles', i.e. just using Riemann's theory of theta functions. ... the 'elementary' approach which is chosen in the book makes it a nice development of Riemann's ideas and accessible to graduate students and young researchers." (Christophe Ritzenthaler, Zentralblatt MATH, Vol. 1222, 2011)

• - Introduction.- 1. Riemann Surfaces.- 2. Zn Curves.- 3. Examples of Thomae Formulae.- 4. Thomae Formulae for Nonsingular Zn Curves.- 5. Thomae Formulae for Singular Zn Curves.-6. Some More Singular Zn Curves.-Appendix A. Constructions and Generalizations for the Nonsingular and Singular Cases.-Appendix B. The Construction and Basepoint Change Formulae for the Symmetric Equation Case.-References.-List of Symbols.-Index.