This course aims to equip graduate students with advanced knowledge of solid state physics that are necessary to understand contemporary literature and conduct frontier research in condensed matter physics and materials science. The course will start with a review of basic structural and electronic properties of crystals, with an emphasis on the band theory of electrons in periodic potentials. Then, the course will move on to thermodynamic and transport properties of metals, including the temperature dependence of specific heat and conductance, and basic magneto-transport properties. In the last part, the course will cover select advanced topics, which may include magnetism, superconductivity, topological band theory, a brief introduction to topological orders, and Berry phase effects in transport properties of the materials.