The second volume of Systemic Functional Linguistics contains Christian M.I.M. Matthiessen’s papers on Systemic Functional Linguistics (SFL) spanning forty years from 1981 to the present. This updated volume builds on the foundation developed in Volume 1, focusing on theoretically guided modelling of language in computational linguistic systems and on key aspects of the theory such as metafunction, rank (the conception of morphology), indeterminacy, and probability. This volume also includes a treatment of systemic functional metatheory – the theory of the nature and applicability of theory. The new chapter written for Volume 2 extends the discussion of the challenge of theorizing language to the challenge of modelling language for neurosemiotics, thus paying attention to the applicability of systemic functional linguistics. This volume captures Matthiessen’s expanding research and addresses core aspects of SFL to help students, instructors, and all readers discover the wealth of Matthiessen’s systemic functional work.