Quantum Mechanics, The Theoretical Minimum
I am delighted so far with Susskind & Friedman‘s book.
It actually has equations!
I have one quibble; as they introduce the notion of dual space they leave the impression that there is a natural map between a space and its dual.
The two spaces are isomorphic but there is no non-trivial automorphism as there is for complex numbers!
Developement here
A footnote on page 33 remarks that in math, basis vectors are not required to be orthonormal while in physics they are.
The difference, I think, is that with a quadratic form it is possible and desirable to require orthonormal.
They smuggled in a quadratic form as they introduced their dual concept.
Raw vectors have no length!