The purpose of this course is to present an investigation of the theoretical and empirical consequences for argument structure of assuming the feature-driven implementation of the Minimalist program (Chomsky, Pesetsky & Torrego). Working with Agree relations between uninterpretable/unvalued and interpretable/valued features, this implementation restricts the occurrence of DP and CP arguments. Investigating argument structure from a syntactic point of view, argument structure is not a result of information and processes residing within the lexicon, but a combination of the architecture of syntax and the meaning of category free roots. The course will take its point of departue in a short introduction to present day research on argument structure and give a brief introduction to the relevant parts of the Minimalist program. The main part of the course will present and discuss the theoretically possible argument structures, given the particular implementation of the minimalist framework argued for.