Book excerpt: Quantification has been at the heart of research in the syntax and semantics of natural language since Aristotle. The last few decades have seen an explosion of detailed studies of the syntax and semantics of quantification and its relation to the rest of the theory of grammar, resulting in a highly sophisticated understanding of the mechanisms of quantification. This book considers the ways natural languages vary with respect to their realisation of quantificational notions. Drawing on data from English, German, Japanese, Korean, Mandarin, Hausa and others, the authors also link the variation in the expression of quantification to the notions of polarity sensitivity, free-choice and indefiniteness.