The central thesis of the book--or at least what I most associate it with--is that progress in a skill like tennis comes primarily from improving one's self-observation.
This isn't the way that Gallwey puts it, but: consider self-evaluation as a supply chain. Its inputs are:
I read Gallwey as making the claims that (1) and (2) are badly underrated; (3) is overrated; and (4) will often happen automatically.
Putting observation before analysis has benefited me across disciplines. In poker, I had what I consider my best World Series of Poker ever (as judged by the average quality of my play) not when my analytical skills were at their peak but when I hit my peak ability to "stay in the moment" and simply describe situations to myself as they happened. The correct betting decisions more or less emerged, unsummoned, after that. Computer people widely acknowledge that simply describing a bug, as precisely as possible, often makes the solution obvious. It's no coincidence that the aforementioned World Series of Poker happened after I'd started seriously training myself as a programmer.
The villain of Inner Game, besides inattention and distraction, is the wrong kind of investment in self-narratives. Here's Galway on abandoning one's preferred style:
The defensive player learns that he can hit winners; the aggressive one finds that he can also be stylish. I have found that when players break their habitual patterns, they can greatly extend the limits of their own style and explore subdued aspects of their personality.
We are over-invested in a kind of conceptual learning that is easier to identify oneself with:
We want to trust Self 1’s conceptual process of learning technique instead of Self 2’s learning from experience. Thinking that it was the obeying of an instruction that produced the good shot, ignoring the role that Self 2 plays, sets us up for disappointment when we give the same instruction yet the same good shot does not occur. Since we think the instruction was correct, the conclusion we come to is that not obeying it led to the error.
Indeed, often people prefer to fail than to achieve a kind of success that feels insufficiently rooted in oneself:
Why would one go back to letting Self 1 control the show if the results were so clearly less effective? I had to search myself for the answer. I realized that there was a distinctly different kind of satisfaction gained in the two methods of hitting the ball. When you try hard to hit the ball correctly, and it goes well, you get a certain kind of ego satisfaction. You feel that you are in control, that you are master of the situation. But when you simply allow the serve to serve itself, it doesn’t seem as if you deserve the credit.
And this ties in to the point that is made so often elsewhere, that when failure is too closely connected to one's sense of self, it's easy to stop trying in order to prevent damage to one's ego:
By not trying, they always have an alibi: "I may have lost, but it doesn’t count because I really didn’t try." What is not usually admitted is the belief that if they had really tried and lost, then yes, that would count. Such a loss would be a measure of their worth. Clearly this belief is the same as that of the competitor trying to prove himself. Both are Self 1 ego trips...
I recommend Inner Game not just as a book about improving specific skills but as an insightful study of self-knowledge more generally. It's also short enough that the reward per page is high.