I have read basic books on Quantum Mechanics like R. Shankar's "Introduction to Quantum Mechanics, Griffiths "Quantum Mechanics" and partly I followed Bransden "Atoms and Molecules".

But none of the above books treat QM in a mathematical way and I am really interested to look into the mathematical side of QM. In doing so, I found a book by Brian C. Hall "Quantum Mechanics for Mathematicians," which treats the subject from Hilbert Space approach and another book I found was by Hermann Weyl "Theory of Groups and Quantum Mechanics" which treats the subject from group theoretic approach.

What is the relation between those two approaches mentioned above and is there any other book which would deem fit for me who has limited mathematical background?