From the introduction to the English edition: ”Singularity theory is still in the state of very rapid development and many new results appeared after the Russian edition of this book. The reader should consult the two volumes of the Arcata singularities conference [Proc. Symp. Pure Math. 40 (1983; Zbl 0509.00008)]; the first author’s works [Russ. Math. Surv. 38, No.2, 87-176 (1983); translation from Usp. Mat. Nauk 38, No.2(230), 77-147 (1983; Zbl 0522.58007); Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 22, 3-55 (1983; Zbl 0537.58012); Catastrophe theory (1984; Zbl 0517.58003); and Z. Ciesielski and C. Olech (eds.), Proc. Int. Congr. Math., Warszawa 1983 (PWN-Polish Sci. Publ., 1984)].
This edition is a careful translation of the Russian one (1982); for a review see Zbl 0513.58001. Birkhäuser has done an excellent job printing this English version and providing thereby to a broad public, having only limited mathematical knowledge (skill in differentiating and some linear algebra and geometry), the basic ideas, methods and results of singularity theory and more applications than are given in previous books on this matter.