The class is an introduction to the study of the complexity of grammatical operations. The first half of the class is an introduction to the formal language theory and automata theory of regular and context free grammars in relation to linguistic issues. In the second part of the class we look at linguistics phenomena that go beyond context free. discuss mildly context sensitive grammar formalisms, and focus on tne role of semilinear growth as a natural constraint on grammars for natural languages.