Introduction
Some background about Galois groups
Basic definitions
Some results about Galois groups over rationals
Various problems related to inverse Galois problem
Methods
Regular Inverse Galois Problem
Hilbert's irreducibility theorem
Noether's problem
Rigidity method
Connections with TGD
Why the inverse Galois problem is so relevant for TGD?
Galois invariance as a physical symmetry in TGD
The physical interpretation of multivariable polynomial rings in TGD
About possible physical implications
Galois groups and genetic code
What is it to be a polynomial of infinite degree?
Conditions for the prime analytic function
Profinite groups and Galois extensions as inverse limits
Could infinite extensions of rationals with a simple Galois group exist?
Two examples
