Since the pioneering works of Frobenius, Schur and Young more than a hundred years ago, the representation theory of the finite symmetric group has grown into a huge body of theory, with many important and deep connections to the representation theory of other groups and algebras as well as with fruitful relations to other areas of mathematics and physics. In this monograph, we present the representation theory of the symmetric group along the new lines developed by several authors, in particular by A. M. Vershik, G. I. Olshanskii and A. Okounkov. The tools/ingredients of this new approach are either completely new, or were not fully understood in their whole importance by previous authors. Such tools/ingredients, that in our book are presented in a fully detailed and exhaustive exposition, are:

1. – the algebras of conjugacy-invariant functions, the algebras of bi-K-invariant functions, the Gelfand pairs and their spherical functions;

2. – the Gelfand–Tsetlin algebras and their corresponding bases;

3. – the branching diagrams, the associated posets and the content of a tableau;

4. – the Young–Jucys–Murphy elements and their spectral analysis;

5. – the characters of the symmetric group viewed as spherical functions.

The first chapter is an introduction to the representation theory of finite groups. The second chapter contains a detailed discussion of the algebras of conjugacy-invariant functions and their relations with Gelfand pairs and Gelfand–Tsetlin bases.