The book "Functional Analysis and the Feynman Operator Calculus" provides a comprehensive mathematical foundation for Feynman operator calculus as well as the Feynman path integral formulation of quantum mechanics. It represents a natural extension of analysis and functional analysis into infinite-dimensional space. The authors, Tepper Gill and Woodford Zachary, present significant results in this work that are used to solve the last two remaining conjectures of Freeman Dyson in quantum electrodynamics. Additionally, it addresses a unification of methods and a relaxation of the requirements for the domain of definition for non-autonomous evolution equations. The book is aimed at advanced students and researchers who wish to engage with the mathematical aspects of quantum mechanics and functional analysis.