Completely revised and expanded new edition covering the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Including new material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilisation and filtering techniques; this text, written by leading experts, is a must-have for students, academics and practitioners in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling.