Number systems include the familiar integers, rationals, reals, etc. as well
as unusual extensions of these sets such as p-adic and hyperreal numbers.
Set Theory - description notation, terminology
(e.g. Cartesian product, power set, cardinality) and construction of sets
The Peano Postulates --
Proving the properties of natural numbers using the Peano Postulates, which
have been formulated so that zero is not included in the set of natural
numbers. (There's quite a debate about this point.)
Introduction to Counting -- explains what
mathematicians mean by "counting" -- that is, putting sets in
one-to-one correspondence.
Construction -- Construction of sets
of numbers, starting with the original Peano Axioms, formulated so that zero is
included in the set of natural numbers. (See Is
Zero a Natural Number?)