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(nl). - 3. Degree of CO-sufficiency. - 4. Sufficiency of jets in Jr(np). - Appendix I Thom's Three Basic Principles. - Appendix II The Proof of Thom's Classification Theorem. - Further Reading. Language: English