This course covers the most important iconic quantum systems, from the hydrogen atom through to solid state systems, focusing on how quantum mechanics is applied and determines physical properties of atoms, molecules, and crystals. It begins with the hydrogen atom, including orbital and spin angular momentum, spin-orbit coupling, and effects of the magnetic field, and then extends to systems of two identical particles: bosons vs. fermions and the helium atom with two electrons. Other topics include spin singlets and triplets, entanglement, perturbation theory, the effects of electron-electron interactions and diatomic molecules. For crystals, the course covers Fermi gases, Fermi surfaces, crystal structure, the reciprocal lattice, the nearly-free electron model, energy bands, and topology using low-dimensional models.