This course we will introduce hydrodynamic theories of active matter. Active matter is driven out of equilibrium by molecular processes and is a model for biological matter. First, we will introduce elementary concepts of hydrodynamic theories and discuss several examples, such as diffusion equation and Navier-Stokes equation. Hydrodynamic equations follow from conservation laws and constitutive equations. We will introduce a theoretical framework to derive consistent constitutive from thermodynamic entropy production near equilibrium. We will then discuss related concepts of Onsager relations and fluctuation-dissipation theorem. We will next show how hydrodynamic theories of active matter systems can be consistently derived using the same framework. Finally, we will study hydrodynamic phenomena in active nematic and chiral fluids, as well as applications of active matter hydrodynamics to biological systems such as surface of biological cells.