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I am looking for books on atomic physics in the 'mathematical style' for advanced undergraduate to graduate level. By 'mathematical style' I mean with definitions clearly labeled (e.g. Definition 1.2: LS-Coupling) along with laws etc. An example from physics would be Nuclear and Particle Physics by W.S.C. Williams. Any recommendations?

Related meta post: How broad can a resource-recommendation question be?

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Quantum spaghettification
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Frankly, I think you will really struggle to find any books in the mathematician's style you exemplify that cover anything close to what I would call actual atomic physics. The closest you're likely to get is books on standard quantum mechanics for mathematicians, along the lines of Faddeev and Takhtajan's texts:

Both of these handle quantum mechanics, going all the way up to some fairly sophisticated QFT, in about as much rigour as is currently known for the results (at about the same tone as V.I. Arnold's Mathematical methods of classical mechanics).

However, they stick to standard quantum mechanics, and they do not go into the nitty-gritty of actual calculations for multi-electron atoms, messy additions of angular momenta, and all the mathematically-boring but experimentally-relevant stuff that makes up actual atomic physics. I see little point in a book that did such a thing, and I suspect most authors in a position to write one would tend to agree.

That said, I really don't see what it is you find so "mathematiciany" about Wiliams' Nuclear and particle physics (besides little boxes on the side with informal and heuristic explanations of the keywords, which add very little to actual rigour), and I don't really see how it is different to solid but standard textbooks like e.g.

or the other recommendations of Book recommendation for Atomic & Molecular physics.

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Emilio Pisanty
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    Maybe mathematical was the wrong word to use. I am very dyslexic (so much so that reading a paragraph let alone a chapter/book is next to useless for me since I won't take it in). I am looking for a book (/books) where I can find information easily without having to read lots of text. When I said mathematical I did not mean 'had lots of maths' or was 'mathematically rigorous' I meant in the layout, such as clear definitions and 'little boxes on the side' so I do not have to read lots of text to get the important information. – Quantum spaghettification Mar 07 '17 at 20:27
  • Then "mathematical" was entirely the wrong word to use. Frankly, if that is what you meant, I would suggest leaving this question as is and asking a separate question where you make that clear and explicit. If what you care about is formatting, then ask explicitly about that, instead of asking a completely different question and expecting people to read your mind. – Emilio Pisanty Mar 07 '17 at 20:34
  • In all fairness I did explain what I meant "By 'mathematical style' I mean with definitions clearly labeled (e.g. Definition 1.2: LS-Coupling) along with laws etc." - what is wrong with this? I thought it was also clear from the example of Williams along with the meta post. – Quantum spaghettification Mar 07 '17 at 20:40
  • By the way feel free to edit the question as you feel appropriate. – Quantum spaghettification Mar 07 '17 at 20:45
  • That it's a completely superficial reading of the term? Mathematical style does have definitions clearly labeled (so you gave no indication that you actually meant something different) but it goes much deeper than that. The question is tenable as is (though as I said what it asks for probably doesn't exist). It is rude to change the core of the questions after you have answers: if you have a separate question, ask separately. – Emilio Pisanty Mar 07 '17 at 20:46