From the reviews: "The main aim of this outstanding research monograph on stochastic differential equations is to introduce a class of points termed isolated singular points. ... The book studies the existence, the uniqueness, and the qualitative behaviour of solutions of singular stochastic differential equations." (Pavel Gapeev, Zentralblatt MATH, Vol. 1071, 2005) "Cherny and Engelbert's book is a research monograph, devoted predominantly to the author's recent deep results, it is written very carefully, in a lucid and precise way, and contains many illustrating examples. The authors have managed to keep it surprisingly self-contained. In my opinion, it is necessary reading for everybody who wishes to understand one-dimensional diffusions thoroughly." (Jan I. Seidler, Mathematical Reviews, Issue 2005 j)

• Introduction.- 1. Stochastic Differential Equations.- 2. One-Sided Classification of Isolated Singular Points.- 3. Two-Sided Classification of Isolated Singular Points.- 4. Classification at Infinity and Global Solutions.- 5. Several Special Cases.- Appendix A: Some Known Facts.- Appendix B: Some Auxiliary Lemmas.- Rferences.- Index of Notation.- Index of Terms.