This text is primarily concerned with the extension of classical results in algebraic topology and related fields (such as homological algebra) to more general settings. The main subjects covered are the rational homology of H-spaces, simplicial spaces and geometric realisation, a construction of Eilenberg-Mac Lane spaces which are abelian topological groups, Whitehead and Postnikov towers utilising these abelian topological groups and the extensibility of local (continuous) group n-cocycles to global groups cocycles resp. the integration of Lie algebra n-cocycles to group n-cocycles.