1. Introduction

  2. Some background about Galois groups

    1. Basic definitions

    2. Some results about Galois groups over rationals

    3. Various problems related to inverse Galois problem

  3. Methods

    1. Regular Inverse Galois Problem

    2. Hilbert's irreducibility theorem

    3. Noether's problem

    4. Rigidity method

  4. Connections with TGD

    1. Why the inverse Galois problem is so relevant for TGD?

    2. Galois invariance as a physical symmetry in TGD

    3. The physical interpretation of multi-variable polynomial rings in TGD

    4. About possible physical implications

    5. Galois groups and genetic code

  5. What is it to be a polynomial of infinite degree?

    1. Conditions for the prime analytic function

    2. Profinite groups and Galois extensions as inverse limits

    3. Could infinite extensions of rationals with a simple Galois group exist?

    4. Two examples