I Introduction.- Organ Transplantation: The Role of Preservation.- An Introduction to the Problems of Organ Cryopreservation.- II Perfusion of Organs with Cryoprotectants: Cooling and Freezing.- Biological Effects of Cryoprotectant Perfusion, Delivery and Removal to Nonfrozen Organs.- Mass Transfer of Liquids across Biological Barriers.- Cytoplasmic Organisation and the Properties of Cell Water: Speculations on Animal Cell Cryopreservation.- Heat Transfer during Cryopreservation.- Ice Crystals in Tissues and Organs.- III Freezing and Vitrification.- Aqueous Solutions: Crystallization, Vitrification and Liquefaction.- Crystallization and Vitrification in Cryoprotected Aqueous Systems.- Ice Crystal Growth in Aqueous Solutions.- Non-Equilibrium Formation of Ice in Aqueous Solutions: Efficiency of Polyalcohol Solutions for Vitrification.- Devitrification and Recrystallization of Glass Forming Aqueous Solutions.- Biological Effects of Vitrification and Devitrification.- IV Electromagnetic Heating.- Electromagnetic Thawing of Organs: A Multidisciplinary Challenge.- Electromagnetic Heating Techniques for Organ Rewarming.- Tissue Heating: Applicator Types and Analysis by Phantom Models.- The Design of an Electromagnetic Rewarming System for Cryopreserved Tissue.- Heat Control and Sensing during Electromagnetic Recovery of Cryopreserved Large Organs.- V Non-Invasive Methods for Studying Organs.- Freezing Patterns in Tissue by NMR Technology.- Nuclear Magnetic Resonance (NMR) Imaging of Perfusion.- Evaluation of Biochemical Processes by NMR.- Examination of Organ Physiology by Positron Emission Tomography.- Contributors.