Publisher Summary This chapter explains constructive order types. The theory of constructive order types constitutes a new approach to the problem of providing a constructive analogue of ordinal number theory. Ordinal number theory may be approached in two ways: (1) ordinals may be considered as being generated in a certain way, and (2) ordinals may be regarded as the equivalence classes of well-ordered sets under (arbitrary) one-one order-preserving maps (isotonisms). The chapter defines constructive order types as equivalence classes of (linear) orderings under effective one-one order-preserving maps (recursive isotonisms). Co-ordinals are the equivalence classes of well-orderings obtained under recursive isotonisms. As there are only denumerably infinitely many recursive isotonisms, co-ordinals are, in general, proper sub-classes of the corresponding classical ordinals.