This volume is a collection of 6 lecture notes presented at the School on Singularity Theory, Sao Carlos, Brazil, July 16-21, 2012, or at the 12th International Workshop on Real and Complex Singularities, Sao Carlos, Brazil, July 22-27, 2012.Topics treated in the 6 lecture notes written by established authors cover, reflecting authors' expertise, 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, Limit cycles of systems of ordinary differential equations.Each lecture note is extremely well-written with plentiful examples and may be considered as one of the most excellent readings in the relevant topic. This book is suitable for being kept at one's desk-side and widely recommended for graduate students studying singularity theory, and researchers in various fields who would like to enjoy the world of singularities.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America