This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.Contents:Some Applications of the Coarea Formula to Partial Differential Equations (F Bethuel & J-M Ghidaglia)Optical Hamiltonian Functions (M Bialy & L Polterovich)On the Geometry of the Hodge-De Rham Laplace Operators (M Craioveanu et al.)Minimal Surfaces in Economic Theory (J Donato)Asymptotic Expansions in Spectral Geometry (P B Gilkey)Deformations and Recursion Operators for Evolution Equations (I S Krasil'shchik & P H M Kersten)Geometric Hamiltonian Forms for the Kadomtsev-Petviashvili and Zabolotskaya-Khokhlov Equations (B A Kupershmidt)Spencer Cohomologies (V Lychagin & L Zilbergleit)Hawking's Radiation via Fourier Integral Operators (P E Parker)Geometry of Super PDE's (A Pràstaro)On a Geometric Approach to an Equation of J d'Alembert (A Pràstaro & Th M Rassias)Geometric Prequantization of the Einstein's Vacuum Field Equations (M Puta)Smooth Marginal Analysis of Bifurcation of Extremals (Y I Sapronov)On the Schrödinger Equation for an N-Electron Atom (C S Sharma)Strings and Membranes (K S Stelle)and other papersReadership: Mathematicians.Key Features:Covers diverse issues and problems of relational world-systems that cannot be fathomed by existing methodologies of economics, ethics, science and societyAttempts to invoke Islamic epistemological foundations in the scientific endeavour and its dissemination in a universal paradigmContains analytical diagrams with new perspectives, keeping in view the critical ideas and issues of economics, ethics, science and society