In this semester, we will study the regularity properties of weak solutions to stationary Navier-Stokes equation and time-dependent Navier-Stokes equation. Since modern regularity theory for Naiver-Stokes flows is based on apriori estimates (in the sense of Lebesgue's L^p space) for higher derivatives of solutions to linear Stokes equation, we will focus on the rigorous derivations of apriori L^2 estimates for higher derivatives of solutions to Stokes equation, either in the stationary or non-stationary setting. After enough preparation at the linear level, we will show how to prove the classical smoothness property of solutions to stationary Navier-Stokes equation. If time permits, we will also demonstrate how to arrive at the classical Serrin-Ladyzhenskaya- Prodi's regularity criteria for solutions to non-stationary Navier-Stokes equation. All and all, we will emphasize the importance of apriori estimates obtained at the linear level in any future studies of regularity problem for solutions to the full Navier-Stokes equation.