Compositionality, by Theo M.V. Janssen (to appear in J.F.A.K. van Benthem & A. ter Meulen (eds), Handbook of Logic and Linguistics, North Holland, Amsterdam) The first topic of the paper is to provide a formalization of the principle of compositionality of meaning. A mathematical model (based upon universal algebra) is presented, and its properties are inverstigated. The second topic is to discuss arguments from the literature against compositionality (of Hintikka, Higginbotham, Pelletier, Partee, Schiffer and others). Methods are presented that help to obtain compositionality. It is argued that the principle should not be considered an empirical verifiable restriction, but a methodological principle that describes how a system for syntax and semantics should be designed. The paper has an appendix by B. Partee on the compositional treatment of genitives.