Memory functions projection operators and the defect technique : some tools of the trade for the condensed matter physicist This book provides a graduate level introduction to three powerful and closely related techniques in condensed matter physics: memory functions projection operators and the defect technique. Memory functions appear in the formalism of the generalized master equations that express the time evolution of probabilities via equations non local in time projection operators allow the extraction of parts of quantities such as the diagonal parts of density matrices in statistical mechanics and the defect technique allows solution of transport equations in which the translational invariance is broken in small regions such as when crystals are doped with impurities. These three methods combined form an immensely useful toolkit for investigations in such disparate areas of physics as excitation in molecular crystals sensitized luminescence charge transport non equilibrium statistical physics vibrational relaxation granular materials NMR and even theoretical ecology. This book explains the three techniques and their interrelated nature along with plenty of illustrative examples. Graduate students beginning to embark on a research project in condensed matter physics will find this book to be a most fruitful source of theoretical training. . Chapter 1. The Memory Function Formalism: What and Why Chapter 2. Zwanzig’s Projection Operators: How They Yield Memories Chapter 3. Building Coarse Graining into Projections and Generalizing Energy Transfer Theory Chapter 4. Relations of Memories to Other Entities and GME Solutions for the Linear Chain Chapter 5. Direct Determination of Frenkel Exciton Coherence from Ronchi Ruling and Transient Grating Experiments Chapter 6. Application to Charges Moving in Crystals: Resolution of the Mobility Puzzle in Naphthalene and Related Results Chapter 7. Projections and Memories for Microscopic Treatment of Vibrational Relaxation Chapter 8. Projection Operators for Various Contexts Chapter 9. Spatial Memories and Granular Compaction Chapter 10. Memories and Projections in Nonlinear Equations of Motion Chapter 11. The Montroll Defect Technique and its Application to Molecular Crystals Chapter 12. The Defect Technique in the Continuum Chapter 13. Memory Functions from Static Disorder: Effective Medium Theory Chapter 14. Effective Medium Theory Application to Molecular Movement in Cell Membranes Chapter 15. A Mathematical Approach to Non Physical Defects Chapter 16. Concluding Remarks.