Good texts on Quantum Mechanics to accompany this online course [duplicate]

I'm a mathematics undergraduate student and I think of studying QM this summer. I've found two online courses given by professor Fredric Schuller QM (link). I look for a good text that I can use to accompany those lectures. I prefer those lectures since they are rigorous unlike most courses I've found on Youtube that are not rigorous enough for my tastes.

Which texts do you recommend? What about Principles of Quantum Mechanics by Shankar? does it go along with the QM course? if not, any other recommendations?

I've suggested the two books since when I skimmed through them, they seemed to be more rigorous than many other texts I skimmed through. Note also that It will be my first course to QM and GR.

Here are the titles of lectures of QM course (every lecture is about 110 minutes):

1. Axioms of Quantum Mechanics

2. Banach Spaces

3. Separable Hilbert spaces

4. Projectors,bars and kets

5. Measure Theory

6. Integration of measurable functions

8. Spectra and perturbation theory

9. Case study: momentum operator

10. Inverse Spectral Theorem

11. Spectral Theorem

12. Stone's theorem & construction of observables

13. Spin

14. Composite systems

15. Total spin of composite system -

16. Quantum Harmonic Oscillator I

17. Quantum Harmonic Oscillator II

18. The Fourier Operator

19. The Schrodinger Operator

20. Periodic potentials I

21. Periodic potentials II

Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

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• This needs to be separated into one post about QM and a separate one about GR. However, note that both of those would probably be duplicates. – DanielSank Jun 3 '16 at 16:36
• Second, please do not expect readers to click on links and read about extra information. If there's something in the links that's important to your question, then include that information directly in the question. If you want to know what book goes with a particular curriculum, include that curriculum in your post. – DanielSank Jun 3 '16 at 16:37
• James Binney at Oxford has an excellent online QM course, and he has the full notes/ transcript of it for free on his website. – user108787 Jun 3 '16 at 16:50
• @DanielSank Tbh I think it was quite fine to have both in the one post, since both courses were given by Frederick Schuller. So what books complement his style/rigour – snulty Jun 4 '16 at 11:46
• @Astring ah good, hopefully you'll get the answer to the original question you asked so! I'm tempted to add some suggestions myself. – snulty Aug 2 '16 at 22:13