Nonnegative matrices and positive operators are widely applied in science, engineering, and technology. This book provides the basic theory and several typical modern science and engineering applications of nonnegative matrices and positive operators, including the fundamental theory, methods, numerical analysis, and applications in the Google search engine, computational molecular dynamics, and wireless communications. Unique features of the book include the combination of the theories of nonnegative matrices and positive operators as well as the emphasis on applications of nonnegative matrices in the numerical analysis of positive operators, such as Markov operators and Frobenius-Perron operators which play key roles in the statistical and stochastic studies of dynamical systems. It can be used as a textbook for an upper undergraduate course in advanced matrix theory and/or positive operators as well as for an advanced topic course in operator theory or ergodic theory. It serves as a good reference for researchers in mathematical sciences, physical sciences, and engineering.