This text is devoted to some analytical and numerical methods for analyzing industrial problems related to emerging technologies such as digital image processing, material sciences and financial derivatives affecting banking and financial institutions. Case studies are based on industrial projects given by reputable industrial organizations of Europe to the Institute of Industrial and Business Mathematics, Kaiserslautern, Germany. Mathematical methods presented in the book which are most reliable for understanding current industrial problems include iterative optimization algorithms, Galerkin's method, finite element method, boundary element method, quasi-Monte Carlo method, wavelet analysis, and fractal analysis. The Black-Scholes model of option pricing, which was awarded the 1997 Nobel Prize in Economics, is presented in the book. In addition, basic concepts related to modelling are incorporated in the book. It should be appropriate for a course in industrial mathematics for upper-level undergraduate or beginning graduate-level students of mathematics or any branch of engineering.