The book provides a general introduction to memory and sleep, focusing on computational understanding of the concepts. It includes both fundamental and advanced topics about the process of learning in biological and computational systems, neurotechnology, NeuroAI, and neuroethics. It systematically covers major categories of memory; neural substrates of memory; brainwaves and their relationship to memory; the role of sleep in memory; dreaming; and memory consolidation. It includes important historical accounts and anecdotes of scientific discoveries. It has fifty-eight illustrations, and hundreds of notes and references. It bridges the gap between memory and computation. It provides novel computational perspectives of brain disorders and mental illnesses. It includes discussions on many computational models such as the attractor network, predictive coding, Bayesian inference, and reinforcement learning. It provides documented clinical observations and patient stories of memory-related diseases (such as amnesia). It discusses stem cells, organoids, memory manipulation, closed-loop neural interfaces, cutting-edge AI, neurotechnology, and their roles in future memory research.