Learning about – Quantum Mechanics – The Nitty-grittyCredits for image original: Tewy.
Professor Frederic P. Schuller has a lecture series where he introduces Quantum Mechanics from a very precise and mathematical point of view. Definition, theorem, proof. The pure state is replaced by a density operator early on so that we can deal with mixed quantum states.
For a quick and condensed introduction to density operators I can recommend these lecture notes by Professor Reinhold Bertlmann.