These are notes from a seminar given at Columbia University
in the year 1971-72. The object is to prove what is herein
christened the Fundamental Theorem of the Representation Theory
of the Symmetric Group. This theorem states that there is an
isomorphism between a ring constructed by composing in a certain
way all the representation rings of the symmetric groups S ,
n
and the ring of all symmetric polynomials in an infinite number
of variables.