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Abstract: In this paper the new techniques and results concerning the structure theory of modules over non-commutative Iwasawa algebras are applied to arithmetic: we study Iwasawa modules over p-adic Lie extensions K of number fields k ``up to pseudo-isomorphism". In particular, a close relationship is revealed between the Selmer group of abelian varieties, the Galois group of the maximal abelian unramified p-extension of K as well as the Galois group of the maximal abelian outside S unramified p-extension where S is a finite set of certain places of k. Moreover, we determine the Galois module structure of local units and other modules arising from Galois cohomology.