[stepstop]

What is an approachable book on Ramsey's theory for non-mathematicians ?

(Graham's number applies to Ramsey's theory.)

[ColinWright]

There's a quick introduction to it here:

https://www.solipsys.co.uk/new/InfiniteRamseyTheorem.html?tg...

That's just a taste of the ideas. For an entire book there's this:

https://www.amazon.com/Ramsey-Theory-2nd-Ronald-Graham/dp/04...

Many books on Graph Theory will have a section about it.