1 Partial Differential Equations and Boundary Value Problems -- On Quaternionic Beltrami Equations -- The Mรถbius Transformation, Green Function and the Degenerate Elliptic Equation -- Quaternionic Analysis in Fluid Mechanics -- 2 singular Integral Operators -- Fourier Theory Under Mรถbius Transformations -- On the Cauchy Type Integral and the Riemann Problem -- Convolution and Maximal Operator Inequalities in Clifford Analysis -- 3 Applications in Geometry and Physics -- A Borel-Pompeiu Formula in ?n and Its Application to Inverse Scattering Theory -- Complex-Distance Potential Theory and Hyperbolic Equations -- Specific Representations for Members of the Holonomy Group -- An Extension of Clifford Analysis Towards Super-symmetry -- The Geometry of Generalized Dirac Operators and the Standard Model of Particle Physics -- 4 Mรถbius Transformations and Monogenic Functions -- The Schwarzian and Mรถbius Transformarions in Higher Dimensions -- The Structure of Monogenic Functions -- On the Radial Part of the Cauchy-Riemann Operator -- Hypercomplex Derivability โ{128}{148} The Characterization of Monogenic Functions in ?n+1 by Their Derivative -- Hypermonogenic Functions -- Reproducing Kernels for Hyperbolic Spaces