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 physics. 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. Next, the course covers a few advanced topics in topological phases of matter, including Berry phases, topological band theory, quantum Hall effects, topological insulators, a brief introduction to topological orders, and Berry phase effect in transport properties of metals.