This volume is a collection of six lecture notes presented at the School on Singularity Theory, São Carlos, Brazil, July 16–21, 2012, or at the 12th International Workshop on Real and Complex Singularities, São Carlos, Brazil, July 22–27, 2012. Topics treated in the six lecture notes written by established authors cover a wide range, including topology and geometry of real singularities, singularities of holomorphic map-germs, singularities of complex algebraic sets, algorithms of the computer algebra “SINGULAR”, singularities of maps and characteristic classes, and limit cycles of systems of ordinary differential equations.

Each lecture note is extremely well written with plenty of examples and may be considered excellent reading on the relevant topic. This book is suitable as a desktop reference and is widely recommended for graduate students studying singularity theory and researchers in various fields who would like to enjoy the world of singularities.