 We have presented a wide range of theories here. The theories motivated by essentially different views of the realm of mathematics (the constructive theories and the theories which support nonstandard analysis) we set to one side. Similarly, the theories motivated by the desire to keep the universe small can be set to one side. The alternative classical set theories which support a fluent development of mathematics seem to be ZFC or its variants with classes (including Ackermann), NFU + Infinity + Choice with suitable strong infinity axioms (to get s.c. sets to behave nicely), and the positive set theory of Esser. Any of these is adequate for the purpose, in our opinion, including the one currently in use. There is no compelling reason for mathematicians to use a different foundation than ZFC; but there is a good reason for mathematicians who have occasion to think about foundations to be aware that there are alternatives; otherwise there is a danger that accidental features of the dominant system of set theory will be mistaken for essential features of any foundation of mathematics. For example, it is frequently said that the universal set (an extension which is actually trivially easy to obtain in a weak set theory) is an inconsistent totality; the actual situation is merely that one cannot have a universal set while assuming Zermelo’s axiom of separation.