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Almost all", "many", "some": fuzzy quantifiers are vital for effective communication in natural language (NL). This monograph pursues an axiomatic method to achieve a reliable interpretation of these quantifiers in technical applications of fuzzy quantification. Unlike existing work in this area, it targets a much broader class of quantificational phenomena which includes all cases usually considered in linguistics. The topics addressed in the monograph run the gamut from the introduction of the theoretical framework for analysing fuzzy quantification, the formalization of semantical requirements on models of fuzzy quantification, the construction and detailed study of prototypical models which conform to the linguistic desiderata, the development of algorithms for implementing the main types of quantifiers in these models, and finally a preview to fuzzy branching quantifications which might be necessary for modelling NL sentences involving more than one quantifier.