Abstract: This paper contains two parts:neurocomputing theory and case studies. The former deuls with some basic concepts of the computation, digital computation, analogy computation, biology computation, neurocomputation, computational energy and optimization theory. The latter illustrates some combinatorial optimization problems mapped on to neural networks including traveling salesman problem, graph partitioning problem, graph vertex cover problem, graph independent set problem,graph maximum clique problem, graph maximum matching problem, graph isomorphism problem, task assignment problem, eight queen problem, A/D converter problem, decomposition/decision problem,linear programming problem and job-shop scheduling problem etc.