Stable Mappings and Their Singularities

I: Preliminaries on Manifolds.- x1. Manifolds.- x2. Differentiable Mappings and Submanifolds.- x3. Tangent Spaces.- x4. Partitions of Unity.- x5. Vector Bundles.- x6. Integration of Vector Fields.- II: Transversality.- x1. Sard's Theorem.- x2. Jet Bundles.- x3. The Whitney C? Topology.- x4. Transversality.- x5. The Whitney Embedding Theorem.- x6. Morse Theory.- x7. The Tubular Neighborhood Theorem.- III: Stable Mappings.- x1. Stable and Infinitesimally Stable Mappings.- x2. Examples.- x3. Immersions with Normal Crossings.- x4. Submersions with Folds.- IV: The Malgrange Preparation Theorem.- x1. The Weierstrass Preparation Theorem.- x2. The Malgrange Preparation Theorem.- x3. The Generalized Malgrange Preparation Theorem.- V: Various Equivalent Notions of Stability.- x1. Another Formulation of Infinitesimal Stability.- x2. Stability Under Deformations.- x3. A Characterization of Trivial Deformations.- x4. Infinitesimal Stability => Stability.- x5. Local Transverse Stability.- x6. Transverse Stability.- x7. Summary.- VI: Classification of Singularities, Part I: The Thom-Boardman Invariants.- x1. The Sr Classification.- x2. The Whitney Theory for Generic Mappings between 2-Manifolds.- x3. The Intrinsic Derivative.- x4. The Sr,s Singularities.- x5. The Thom-Boardman Stratification.- x6. Stable Maps Are Not Dense.- VII: Classification of Singularities, Part II: The Local Ring of a Singularity.- x1. Introduction.- x2. Finite Mappings.- x3. Contact Classes and Morin Singularities.- x4. Canonical Forms for Morin Singularities.- x5. Umbilics.- x6. Stable Mappings in Low Dimensions.- xA. Lie Groups.- Symbol Index.