This monograph has been written with the primary objective of addressing the rapid development in the knowledge of topological fixed point and spectral theories. It covers various aspects of the mathematical theory of linear and nonlinear operators, with a particular focus on fixed point theory in Banach spaces for different types of single-valued operators and spectral theory for positive operators. Such results are essential tools for demonstrating the existence of solutions to various mathematical models, including differential, integral, and partial differential equations, which represent phenomena arising in fields such as neutron transport theory and growing cell populations. This monograph, along with the recent references it contains, will be of great assistance to young researchers in fixed point and spectral theories and those interested in these fields of study.