This book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.

Notations.- Preface to the first edition.- Preface to the second Edition.- Introduction to soft matter.- Discovery of soft-matter quasicrystals and their properties.- Brief review on elasticity and hydrodynamics of solid quasicrystals.- Case study of equation of state of several structured fluids.- Poisson bracket method and equations of motion of soft-matter quasicrystals.- Oseen theory and Oseen solution.- Dynamics of soft-matter quasicrystals with 12-fold symmetry.- Dynamics of 10-fold symmetrical soft-matter quasicrystals.- Dynamics of possible soft-matter quasicrystals with 8-fold symmetry.- Dynamics of soft-matter quasicrystals with 18-fold symmetry.- Dynamics of possible soft-matter quasicrystals with 7-, 9- and 14-fold symmetries.- Re-discussion on symmetry breaking and elementary excitations concerning quasicrystals.- An application to thermodynamic stability of soft-matter quasicrystals.- Applications to device physics: photon band-gap of holographic photonic quasicrystals.-Possible applications to general soft matter.- Applications to smectic-A liquid crystals, dislocation and crack.- Conclusion remarks