Includes bibliographical references (p. 135-136) and index.
Introduction -- Prolongations of integral curves. Regular, vertical, and critical curves and points -- RVT classes. RVT codes of plane curves. RVT and Puiseux -- Monsterization and legendrization. Reduction theorems -- Reduction algorithm. Examples of classification results -- Determination of simple points -- Local coordinate systems on the Monster -- Prolongations and directional blow-up. Proof of Theorems A and B -- Open questions -- Appendix A. Classification of integral Engel curves -- Appendix B. Contact classification of Legendrian curves -- Appendix C. Critical, singular and rigid curves.