Preface; Overview; 1. Spectral Theory for Hilbert Space Operators; 2. Ext(X) as a Semigroup with Identity; 3. Splitting and the Mayer-Vietoris Sequence; 4. Determination of Ext(X); 5. Applications to Operator Theory; 6. Epilogue; Appendix A. Point Set Topology; Appendix B. Linear Analysis; Appendix C. The Spectral Theorem; Subject Index; Index of Symbols; References.