He also simplifies an explanation of why algorithmic design vs "all at once" may be preferable: an algorithm offers opportunities for discovery beyond intuition and memory. In other words, trust the process.
My daughter goes to UO, where Alexander had a hand in applying some of his ideas. If you go to the campus today, though, it's overwhelmingly Uncle Phil who shapes the look and feel, sadly.
I do second the recommendation to read the other works as well. If pairing one book with Pattern, I would choose The Battle for the Life and Beauty of the Earth because it most clearly portrays the process of taking Alexander’s thinking into the real world and overcoming its perverse incentives to impose ugliness and financial difficulty. I gave a talk for a bunch of developers immediately after reading it because it mapped so well to what we do and struggle with.
Anyway, in the actual practice of architecture, A Pattern Language is by far the best of the set. There are other books that make approximately the same case as Timeless Way of Building.  Most of it's fame is from standing in relation to A Pattern Language.
 e.g. How Buildings Learn, The Timeless Way of Seeing, Structure of the Ordinary, etc.
I was aware that there was a trilogy, chose to dig into “Pattern” first, and got a lot out of it.
Following the patterns without understanding the philosophy makes no sense to me because it’s a very opinionated and, in the modern world, quite radical. What if you don’t agree with it? I think many don’t. At least, you want to be able to read them critically.