chapter 1 G eometry o f Si ngul a ri ti es -- chapter 2 Elliptic O perators on Si ngul ar Mani folds -- chapter 3 Pseudodifferential Operators -- chapter 4 Localization (Surgery) in Elliptic Theory -- chapter 5 I ndex Theo ry -- chapter 6 Elliptic Edge Problems -- chapter 7 Fourier Integral Operators on Si ng ul ar Mani fo lds -- chapter 8 Rel ative Elliptic Theory -- chapter 9 I ndex ofG eo metri c O pera to rs o n Ma ni fo l ds w i th Cyli ndri ca l Ends -- chapter 10 Homotopy Classification of Elliptic O perators -- chapter 11 Lefschetz Formulas -- chapter Appendix A Spectral Flow -- chapter Appendix B Eta Invariants -- chapter 100 Appendix C Index of Parameter-Dependent Elliptic Families -- chapter Bi bliographi c Remarks -- chapter Bi bliography.