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This book presents a concise and rigorous exposition of Preisach hysteresis models and their applications to the modeling of neural memory. It demonstrates that memory of Preisach hysteresis models mimics such properties as: selective nature of neural memories extracted from sensory inputs, distributed nature of neural memories and their engrams, neural memory formation as an emerging property of sparse connectivity, neural memory stability with respect to protein turnover, neural memory storage plasticity and neural memory recalls and their effect on storage. The text is designed to be accessible and appealing to a broad audience of neuroscientists, biologists, bioengineers, electrical engineers, applied mathematicians and physicists interested in neural memory and its molecular basis.