This is the Part 2 of the paper about an axiomatic theory of universes called “universics”. Two main results are presented here: (1) a generalization of the notion “well-founded set” to the notion “well-founded universe” and the proof of a theorem saying that the theory W introduced in Part 1 axiomatizes the class of well-founded universes, and (2) an algebraic set theory based on the ideas of universics, into which set theory can be immersed. This is contended to achieve the Harvey Friedman desideratum to find an alternative theory pivoted around induction, into which set theory or a large part of it could be immersed.