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Computational and network aspects of the brain are explored. The topics covered include structure, operation and connectivity of neurons, general network structure of the neural system, and the connectivity constraints imposed by pre- and post-natal neural development and the desirability of network consistency within a species. Both discrete and continuous aspects of neural computation are covered. Precise mathematical tools and analyses such as logic design, transient and steady state behavior of linear systems, and time and connectivity randomization are discussed. The concepts are illustrated with several applications. Memory formation from the synaptic level to the high level constructs are explored. Students are not expected to master any of the mathematical techniques but are expected to develop a strong qualitative appreciation of their power. Cerebellum, which has a simple network connectivity, will be covered as a typical system. Recommended course background: linear algebra, differential equations, probability, and algorithms.