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This monograph has been written with a prime objective to take care of the fast paced development in the knowledge of Topological Fixed Point and Spectral Theories. This monograph covers various aspects of Mathematical theory of linear and nonlinear operators and focuses especially on fixed point theory in Banach spaces for different kinds of single-valued operators and spectral theory for positive operators. Such results are very important tools for provoing the existence of solutions to various mathematical models (differential, integral and partial differential equations etc) representing phenomena arising in different fields such the neutron transport theory and growing cell populations. This monograph and the recent references in, will be of great help for the young researchers in fixed point and spectral theories and those intetrested in these fields of study.