Table of Contents

1 Introduction to Singularity Theory with Historical Remarks.- 1. Introduction with naive discussion.- 2. Elementary definitions.- 3. Genericity.- 4. Stability.- 5. Singularities.- 2 On Singularities of Mappings from the Plane into the Plane.- 1. Introduction.- 2. Jet spaces.- 3. Transversality.- 4. Morse Lemma — the genericity aspect.- 5. Characterization of folds and cusps.- 6. Whitney’s Theorem.- 7. The proof of Theorem 6.1.- 8. The proof of Theorem 6.2.- 3 Unfoldings of Mappings.- 1. Introduction.- 2. Germs of mappings.- 3. Finitely determined germs.- 4. Universal unfolding.- 5. Thom’s Classification Theorem.- 4 Catastrophe Theory.- 1. Introduction.- 2. Naive discussion with illustrative examples.- 3. The elementary catastrophes.- 4. Types of elementary catastrophes.- 5 Thom-Whitney Stratification Theory.- 1. Introduction.- 2. Examples.- 3. Regularity conditions of H. Whitney.- 4. Fundamental theorems.- 5. Ratio test.- 6 CO-Sufficiency of Jets.- 1. Introduction.- 2. Criterion of CO- and v-sufficiency of jets in Jr(n,l).- 3. Degree of CO-sufficiency.- 4. Sufficiency of jets in Jr(n,p).- Appendix I — Thom’s Three Basic Principles.- Appendix II — The Proof of Thom’s Classification Theorem.- Further Reading.