In the book *Ramsey Theory* by Graham, Rothschild and Spencer the authors state:

The Hales Jewett Theorem strips van der Waerden's theorem of its unessential elements and reveals the heart of Ramsey theory. It provides a focal point from which many of the results can be derived and acts as a cornerstone of much of the more advanced work. Without this result Ramsey theory would more properly be called Ramseyian theorems.

I am interested in knowing as to what further advanced results flow from the Hales Jewett theorem and why is the theorem so crucial.

Thanks for your time.