I'm planning on doing some reading projects that lie a little above the undergraduate curriculum. To be more specific, I'm a physics major and I plan on doing reading projects in a few advanced physics topics (eg. Feynman path integral formulation of quantum mechanics, statistical mechanics and nonlinear dynamics) and math (eg. group theory, knot theory and complex analysis). I plan on majoring in theoretical physics for my masters where these concepts are very much relevant. Will an admissions committee view this in a positive light? Will this be a good addition to my CV?
Whether it is during your interview, or when they read you SoP, there will always read your enthusiasm between the lines. If you happen to be doing some self-study by yourself, it clearly shows that you are personally interested in the subject and enthusiastic about it.
Plus, by doing undertaking such projects, you will have a much wider perspective about the field and you will be familiar with more complex ideas. So, when they ask you "why do you want to work on this field", you can give a much more specific answer than "I find it interesting".
A reading program directed by a professor who will somehow examine you on what you have learned is one thing, especially if it comes with a formal evaluation. But a private reading program that has no validation element isn't going to help in admissions or on a CV.
It is something you could mention in an interview, I think, but you would be immediately asked some question about what you have learned from it. You will need to show that you gained some insight from your readings.
That's not to say it isn't a good thing to do, but its face value (to another) is essentially zero with no external evaluation. But if it gives you insight then it will be good for your career in the long run even if you can't show in on paper.