1. Introduction

2. Preliminaries

3. Igusa-Todorov functions

5. Selective algebras, Frobenius extensions, and Gorenstein algebras

6. Characterization of the IT-function $\phi$ by the bifunctors Ext and Tor

8. Algebras of $\Omega^{\infty}$-infinite representation type

9. The symmetry problem

10. Generalizations