Preface; Addresses of contributors; List of participants; Part I. The Local Homological Conjectures, Big Cohen-Macaulay Modules, and Related Topics: 1. The syzygy problem: a new proof and historical perspective E. G. Evans and Phillip Griffith; 2. The theory of homological dimensions of complexes Hans-Bjorn Foxby; 3. Complexes of injective modules Hans-Bjorn Foxby; 4. The local homological conjectures Melvin Hochster; 5. The rank of a module G. Horrocks; 6. Modules of generalized fractions and balanced big Cohen-Macaulay modules R. Y. Sharp and H. Zakeri; 7. Sur la theorie des complexes parfaits L. Szpiro; Part II. Determinantal Ideals, Finite Free Resolutions, and Related Topics: 8. Some exact complexes and filtrations related to certain special Young diagrams Kaan Ankin and David A. Buschsbaum; 9. The canonical module of a determinantal ring Winfried Bruns; 10. The MacRae invariant Hans-Bjorn Foxby; 11. Finite free resolutions and some basic concepts of commutative algebra D. G. Northcott; Part III. Multiplicity Theory, Hilbert and Poincare Series, Associated Graded Rings, and Related Topics: 12. Blowing-up of Buschsbaum rings Shiro Goto; 13. Necessary conditions for an analytical algebra to be strict J. Herzog; 14. Multiplicities, Hilbert functions and degree functions D. Rees; 15. Finiteness conditions in commutative algebra and solution of a problem of Vasconcelos Jan-Erik Roos; 16. On the use of graded Lie algebras in the theory of local tings Jan-Erik Roos; 17. Reductions, local cohomology and Hilbert functions of local rings Judith D. Sally; Further problems.