Logic.- Elementary arithmetic.- Species.- Sequences and constructive (lawlike) objects.- Elementary theory of real numbers.- Ordering relations and order on the real line.- Constructive or lawlike analysis.- Lawless sequences of natural numbers.

- Choice sequences.- Spreads and a theory of real numbers.- Topology; separable metric spaces.- Applications of the continuity principles and the fan theorem.- Well-orderings and ordinals.- Species revisited; the role of the comprehension principle.- Brouwer's theory of the creative subject.