In which various examples are given to illustrate the problems and techniques of constructive algebra. As in Chapter 2, particular attention is paid to results whose classical counterparts are either routine or trivial, but whose constructive proof requires careful choice of definitions and hypotheses, and subtle technique. For example, in Section 6 there is given a constructive version of the Hilbert basis theorem, for which we need both the correct definition of a Noetherian ring, and the classically redundant hypothesis of coherence. The relationship between constructive and recursive algebra is illustrated in Section 4, which deals with the question of the uniqueness of splitting fields.