 Once pairs are defined, the definition of relations and functions proceeds exactly as in the usual set theory. The definitions of integers and rational numbers present no problem, and the Dedekind construction of the reals can be carried out as usual. We will focus here on developing the solutions to the paradoxes of Cantor and Burali-Forti in NFU, which give a good picture of the odd character of this set theory, and also set things up nicely for a brief discussion of natural strong axioms of infinity for NFU. It is important to realize as we read the ways in which NFU evades the paradoxes that this evasion is successful: NFU is known to be consistent if the usual set theory is consistent, and close examination of the models of NFU shows exactly why these apparent dodges work.