The first edition has been reviewed, see Zbl 0755.03029. The changes to the second edition are mostly fairly minor – a little re-writing, and a mention made of the relevant papers that have appeared in the literature in the four years between the two editions. The extensive bibliography on set theory with a universal set has been updated and expanded. The main changes in the second edition come in Chapter 4, previously eleven pages entitled “Interpretations in well-founded set theories” now expanded to twenty pages and entitled “Church-Oswald models”. The new material in this chapter discusses a fairly general construction of models of various set theories with a universal set inside ZF, of which constructions of A. Church [Proc. Symp. Pure Math. 25, 297-308 (1974; Zbl 0317.02079)] and U. Oswald [in his Ph.D. thesis, 1976]can be viewed as particular cases.