José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests are in Algebraic and Differential Topology, Differential Geometry and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.Dũng Tráng Lê (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975—1999)  and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, carousels, among other topics.José Seade (DPhil, University of Oxford 1980) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His researchis in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor’s fibration theorem for analytic maps. In 2007 he was awarded the Ferran Sunyer i Ballaguer prize.

• Foreword.- Preface.- 1 The Combinatorics of Plane Curve Singularities.- 2 The Topology of Surface Singularities.- 3 Resolution of Singularities: an Introduction.- 4 Stratification Theory.- 5 Morse Theory, Stratification and Sheaves.- 6 The Topology of the Milnor Fibration.- 7 Deformation and Smoothing of Singularities.- 8 Distinguished Bases and Monodromy of Complex Hypersurface Singularities.- 9 The Lefschetz Theorem for Hyperplane Sections.- 10 Finite Dimensional Lie Algebras in Singularities. -Index.

José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests are in Algebraic and Differential Topology, Differential Geometry and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.Dũng Tráng Lê (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975—1999)  and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, carousels, among other topics.José Seade (DPhil, University of Oxford 1980) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His researchis in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor’s fibration theorem for analytic maps. In 2007 he was awarded the Ferran Sunyer i Ballaguer prize.

• Foreword.- Preface.- 1 The Combinatorics of Plane Curve Singularities.- 2 The Topology of Surface Singularities.- 3 Resolution of Singularities: an Introduction.- 4 Stratification Theory.- 5 Morse Theory, Stratification and Sheaves.- 6 The Topology of the Milnor Fibration.- 7 Deformation and Smoothing of Singularities.- 8 Distinguished Bases and Monodromy of Complex Hypersurface Singularities.- 9 The Lefschetz Theorem for Hyperplane Sections.- 10 Finite Dimensional Lie Algebras in Singularities. -Index.

José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests are in Algebraic and Differential Topology, Differential Geometry and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.Dũng Tráng Lê (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975—1999)  and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, carousels, among other topics.José Seade (DPhil, University of Oxford 1980) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His researchis in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor’s fibration theorem for analytic maps. In 2007 he was awarded the Ferran Sunyer i Ballaguer prize.

• Foreword.- Preface.- 1 The Combinatorics of Plane Curve Singularities.- 2 The Topology of Surface Singularities.- 3 Resolution of Singularities: an Introduction.- 4 Stratification Theory.- 5 Morse Theory, Stratification and Sheaves.- 6 The Topology of the Milnor Fibration.- 7 Deformation and Smoothing of Singularities.- 8 Distinguished Bases and Monodromy of Complex Hypersurface Singularities.- 9 The Lefschetz Theorem for Hyperplane Sections.- 10 Finite Dimensional Lie Algebras in Singularities. -Index.