This is an extraordinary monograph, one of the few not to be missed by anybody deeply interested in stochastic financial modelling. It demonstrates in a rather striking manner how concepts and techniques of modern theoretical physics (such as non-Euclidean geometry, supersymmetric quantum mechanics, path integrals and functional derivatives) may be applied to mathematical finance and option pricing theory. Some of the techniques mentioned above have already been known in the financial literature separately under different names. However, it also presents original ideas never before published by researchers in finance. The monograph builds an original bridge to connect analysis, geometry and probability together with stochastic finance, a bridge supported both by very advanced mathematics and imagination. Mathematica and C++ are used for numerical implementation and many end-of-chapter problems lead the reader to recently published papers.