This book applies the mathematics and concepts of quantum mechanics and quantum field theory to the modelling of interest rates and the theory of options. Particular emphasis is placed on path integrals and Hamiltonians. Financial mathematics is currently almost completely dominated by stochastic calculus. The present book is unique in that it offers a formulation that is completely independent of that approach. As such many new results emerge from the ideas developed by the author. This pioneering work will be of interest to physicists and mathematicians working in the field of finance, to quantitative analysts in banks and finance firms and to practitioners in the field of fixed income securities and foreign exchange. The book can also be used as a graduate text for courses in financial physics and financial mathematics.