Mathematical models can be used to address many of the challenges and opportunities presented by modern biology. The description of biological phenomena requires a variety of mathematical theories, particularly in the emerging field of systems biology. "Mathematical Methods in Biology and Neurobiology" systematically introduces and further develops these mathematical structures and methods. It examines discrete structures and graph theory, stochastic processes, dynamical systems, and partial differential equations, as well as optimization and calculus of variations. The biological applications range from molecular to evolutionary and ecological levels, including kinetic reactions in cells and gene regulation, biological pattern formation and chemotaxis, the biophysics and dynamics of neurons, information coding in neural systems, and the reconstruction of phylogenetic trees.