Noam Chomsky's definition... «Linguistics: A Very Short Introduction »

Noam Chomsky's definition in the 1950s is a classic formulation, and in practice this view is still fruitful.

I will consider a language to be a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements …

The fundamental aim in the linguistic analysis of a language L is to separate the grammatical sequences which are the sentences of L from the ungrammatical sequences which are not sentences of L and to study the structure of the grammatical sequences. The grammar of L will thus be a device that generates all of the grammatical sequences of L and none of the ungrammatical ones.

(Noam Chomsky, 1957)

Another view, however, sees the ‘language’ as the system itself.