This book contains the contributions by the participants in the nine of a series of workshops. Throughout the series of workshops, the contributors are consistently aiming at higher achievements of studies of the current topics in complex analysis, differential geometry and mathematical physics and further in any intermediate areas, with expectation of discovery of new research directions. Concerning the present one, it is worthwhile to mention that, in addition to the new developments of the traditional trends, many attractive and pioneering works were presented and their results were contributed to the present volume. The contents of this volume therefore will provide not only significant and useful information for researchers in complex analysis, differential geometry and mathematical physics (including their related areas), but also interesting mathematics for non-specialists and a broad audience. The present volume contains new developments and trends in the studies on constructions of holomorphic Cliffordian functions; the swelling constructions of minimal surfaces with higher genus in flat tori; the spectral properties of soliton equations on symmetric spaces; new types of shallow water waves described by Camassa–Holm type equations, the properties of pseudo-hermitian boson and fermion coherent states; fractals and chaos on orthorhombic lattices, and even an ambitious proposal of a graph model for Kaehler manifolds with Kaehler magnetic fields.Contents:A Discrete Model for Kähler Magnetic Fields on a Complex Hyperbolic Space (T Adachi)Generalizations of Conjugate Connections (O Calin et al.)Cyclic Hyper-Scalar Systems (S Dimiev et al.)Relativistic Strain and Electromagnetic Photon-Like Objects (S Donev & M Tashkova)Persistence of Solutions for Some Integrable Shallow Water Equations (D Henry)Heisenberg Relations in the General Case (B Z Iliev)Poisson Structures of Equations Associated with Groups of Diffeomorphisms (R I Ivanov)Hyperbolic Gauss Maps and Parallel Surfaces in Hyperbolic Three-Space (M Kokubu)On the Lax Pair for Two and Three Wave Interaction System (N A Kostov)Mathematical Outlook of Fractals and Chaos Related to Simple Orthorhombic Ising–Onsager–Zhang Lattices (J Ławrynowicz et al.)A Characterization of Clifford Minimal Hypersurfaces of a Sphere in Terms of Their Geodesics (S Maeda)A Short Note on the Double-Complex Laplace Operator (P Popivanov)Monogenic, Hypermonogenic and Holomorphic Cliffordian Functions — A Survey (I P Ramadanoff)New Integrable Equations of mKdV Type (T I Valchev)and other papersReadership: Graduate students and researchers in analysis, differential geometry and mathematical physics including their intermediate fields.