We will describe an quantitative approach for solving the Boltzmann equation in the kinetic theory. The approach has been developed, with Shih-Hsien Yu, in the past decade and proven effective in understanding some of the important physical phenomena. It is based on the explicit construction of the Green's function for the linearized Boltzmann equation. We will describe the key steps of this construction, revealing the particle-fluid duality of the Boltzmann equation. Boltzmann equation is derived from the Newtonian particle system and differs from the fluid dynamics equations such as the Euler and Navier-Stokes equations in several essential aspects. It can model boundary physical effects closer to the first principle than the fluid dynamics can. We will illustrate these by applying the Green's function approach to the analysis of boundary layers and interior nonlinear waves. The only prerequisite for this talk is multi-variables calculus.