Responding to the growing demand for rigorous modeling frameworks capable of addressing complex technological challenges across disciplines, this book offers a coherent panorama of contemporary methodologies. These span lossless image compression algorithms, electrical impedance tomography and extragradient methods for variational inequalities in Banach spaces. It further examines multiphysics modeling in environmental engineering, grid-supported magnetic levitation systems and the optimization of water transport in porous media for sustainable irrigation. Foundational stochastic tools - such as gamma processes and hidden Markov models for reliability and maintenance planning - are integrated with theoretical advances, including matrix polynomials on noncommutative sets.