This book gives a self-contained fundamental study of the subject. Besides the following special features it contains the author's detailed solution to the long-standing unsolved problem in the theory of complex manifolds: Does there exist a complex structure on the six-sphere? The special features of the book are: a classification of almost complex (and similarly, almost Hermitian) structures together with inclusion relations; discussions about various known almost Hermitian structures; a necessary and sufficient condition for a general almost Hermitian manifold to have constant holomorphic sectional (or bisectional) curvature and similar conditions for various special almost Hermitian manifolds; some complex Laplacians together with some of their relationships with the real Laplacian; the spectral geometry of Riemannian manifolds and some general almost Hermitian manifolds including Kählerian manifolds as a special case; conditions for an almost complex structure to be a complex structure; some vanishing theorems for Riemannian and almost Hermitian manifolds.Contents:Riemannian StructuresAlmost Complex StructuresAlmost Hermitian StructuresThe Real LaplacianComplex LaplaciansComplex StructuresVanishing TheoremsReadership: Mathematicians and graduate students in mathematics.Key Features:Discusses in-depth a topical subject, treated with the very latest informationWritten by leading contributors in the field, with the world-renowned Professor Dame Julia Polak as the lead editorContains an array of color diagrams and illustrationsDiffers from competing titles in that its coverage ranges from the basic science of stem cells and biomaterials to clinical applications, policy issues, views from the commercial sector and many others