It is interested in describing the formal and semantic characteristics of language in separation from sociology, psychology or neurobiology, and has a high degree of logical rigour.

[6]: 168  He received a doctorate in comparative Indo-European philology for his Études baltiques from 1932,[6]: 169  and later took over Holger Pedersen's chair in Copenhagen after having been in Aarhus from 1934 to 1937.

Membership of the group grew rapidly and a significant list of publications resulted, including an irregular series of larger works under the name Travaux du Cercle Linguistique de Copenhague.

[8] The Linguist Circle of Copenhagen still exists today and arranges seminars, publishes Acta Linguistica Hafniensia and runs subcommittees.

His first major book, Principes de grammaire générale, which he finished in 1928, is an invaluable source for anyone interested in Hjelmslev's work.

In this book, Hjelmslev analysed the general category of case in detail, providing ample empirical material supporting his hypotheses.

[10] His most well-known book, Omkring sprogteoriens grundlæggelse, or in English translation, Prolegomena to a Theory of Language, first published in 1943, critiques the then-prevailing methodologies in linguistics as being descriptive, even anecdotal, and not systematising.

Not only do pictures and literature manifest the same organising principles, but, more broadly, seeing and hearing, though certainly not identical, interact in surprisingly complex ways at deeper levels of the sign hierarchy which Hjelmslev sought to understand.

Most conspicuously, Hjelmslev's lines of inquiry have been taken up by Gilles Deleuze and Félix Guattari (see the "Postulates of Linguistics" and "Geology of Morals" chapters of A Thousand Plateaus), and subsequently their followers.

Hjelmslev introduced the terms glosseme, ceneme, prosodeme and plereme as linguistic units, analogous to phoneme, morpheme, etc.