Raimundo Nonato Araújo dos Santos is an Associate Professor at the Institute of Mathematics and Computer Sciences of the University of São Paulo, Brazil. He holds a PhD in Mathematics (Singularity Theory) from the University of São Paulo (2002), with studies in Catastrophe Theory at the Northeastern University, in the USA. His research is on the fields of geometry and topology of real and complex singularities, real and complex Milnor fibrations, and topology of polynomial mappings at infinity.Aurelio Menegon Neto is an Adjunct Professor at the Federal University of Paraíba, Brazil. He holds a PhD in Mathematics from the National Autonomous University of Mexico (UNAM) and did post-doc studies at the Institute of Mathematics and Computer Sciences of the University of São Paulo, Brazil, and UNAM, Mexico. His field of research is Singularity Theory, more specifically on the topology of real and complex manifolds and singularities in differential applications.David Mond is a Full Professor at the Mathematics Institute of the University of Warwick, England. He did his PhD in Liverpool (1982), England, and has held several appointments in institutions such as University of Los Andes (Colombia), National University (Colombia), University of Seville (Spain) and Institut des Hautes Etudes Scientifiques (France). He is also co-editor of "Singularity Theory and its Applications", published with Springer, and has published over 40 papers and lecture notes on this field.Marcelo J. Saia is a Full Professor at the Institute of Mathematics and Computer Sciences of the University of São Paulo, Brazil. He did his PhD at the University of São Paulo (1991), with studies at the University of Liverpool, England. His current research is focused on Singularity and Catastrophe Theory, more specifically on singularities of differential applications; singularities, dynamical systems and geometry; and topology of singular manifolds.Jawad Snoussi isa Full Researcher at the Institute of Mathematics of the National Autonomous University of Mexico (UNAM). He doctored in Mathematics at University of Provence (Aix-Marseille 1), France, in 1998, with studies at the Institute of Mathematics and Computer Sciences of the University of São Paulo, Brazil; at the Institute of Mathematics of the UNAM, Mexico; at the University of Lisbon, Portugal; and at the Internacional Center for Theoretical Physics, Italy. His research field is the local study of singularities of complex analytic spaces and real and complex analytic maps.

• Chapter 1. Combinatorial Models in the Topological Classification of Singularities of Mappings (J.J. Nuno-Ballesteros).- Chapter 2. Topology of real singularities (Nicolas Dutertre).- Chapter 3. Equisingularity and the Theory of Integral Closure (Terence Gaffney).- Chapter 4. A Brief Survey on Singularities of Geodesic Flows in Smooth Signature Changing Metrics on 2-Surfaces (N.G. Pavlova).- Chapter 5. Orbital Formal Rigidity for Germs of Holomorphic and Real Analytic Vector Fields (Jessica Angelica Jaurez-Rosas).