The book is about strong axioms of infi nity in set theory (also known as large cardinal
axioms) and the ongoing search for natural models of these axioms. Assuming the Ultrapower
Axiom a combinatorial principle conjectured to hold in all such natural models we solve
various classical problems in set theory (for example the Generalized Continuum Hypothesis)
and uncover a theory of large cardinals that is much clearer than the one that can be developed
using only the standard axioms.
