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* Front matter * Introduction 7 * 1 General arrangements 11 * 1.1 Diagrams of spaces 11 * 1.2 Diagrams of chain complexes 15 * 1.3 Arrangements 22 * 2 Linear and related arrangements 33 * 2.1 Homology and Homotopy 33 * 2.2 Products 52 * 2.3 Products in projective arrangements 58 * 2.4 Projective c-arrangements 68 * Bibliography 77 ; This thesis is concerned with homotopy and homology properties of subspace arrangements. An arrangement A in a topological space X is a finite set of subspaces of X. A goal in the study of arrangements is the description of the union and the complement of A. The main result of this work is the description of the cohomology ring of the complement of an arrangement of linear subspaces of a complex projective space. Since the additive structure of the ring has been determined by Goresky and MacPherson, this amounts to determining cup products. This is done by a formula of the kind which for affine arrangements has been given and proved for rational coefficients by Yuzvinsky. It is presented in a form in which it has in the affine case been proved for integral coefficients and generalized to certain real arrangements by de Longueville and the author. The first chapter is concerned with arrangements in topological spaces in general. It starts with a brief presentation of results on diagrams of spaces that have been seen to be useful in the study of homotopy properties of arrangements by Ziegler and Živaljević. We then develop an analogous theory of diagrams of chain complexes which gives some additional flexibility in the study of homology properties of arrangements. This introduces the spectral sequence that we use in the last section of the first chapter to derive a product formula for the cohomology ring of an arrangement in a manifold. Due to its generality this formula cannot describe the ring completely. It is graded in the sense that it determines products only up to terms of lower degree in the defining filtration of the spectral sequence. The second chapter deals with linear ...