Dive deep into the foundations of quantum mechanics through this comprehensive lecture series. Explore key concepts including axioms of quantum mechanics, Banach spaces, Hilbert spaces, and measure theory. Progress to advanced topics such as self-adjoint operators, spectral theory, and perturbation theory. Examine practical applications with case studies on momentum operators, spin systems, and composite systems. Delve into the quantum harmonic oscillator, Fourier operators, and Schrödinger operators. Conclude with an in-depth look at periodic potentials. Gain a thorough understanding of quantum theory from Professor Frederic Schuller over 21 lectures, providing a solid mathematical foundation for further study in quantum physics.