Rarefied gas flows are ubiquitous in aerospace and modern industry, such as the reentry of spaceship into the atmosphere, micro-electromechanical systems, and shale gas extraction. Its advance in science and technology is crucial to the national defence as well as the economical and societal developments. Due to the rapid development in aerospace sector and the huge demand in vacuum technology in big companies such as Huawei, this elective course is tailored for the students in the Department of Mechanics and Aerospace Engineering dedicated to the introduction of fundamental theory and numerical methods in rarefied gas dynamics. It is hoped that after completing this course the students will have basic knowledge and skills in rarefied gas dynamics. Topics covered include the breakdown of Navier-Stokes equations, wide range applications of rarefied gas dynamics, derivation of the Boltzmann equation and its relation to the Navier-Stokes equations, the kinetic modelling of monatomic and polyatomic gas, and the typical numerical methods and applications. In addition to the theoretical deduction in classroom teaching, this course will provide several numerical simulation codes for the students to better understand the rarefied gas dynamics.