Convex geometric analysis is closely related to differential geometry and integral geometry, it is one subject that studies geometric structures and invariants of convex sets. In this mini-course, I will discuss both the classical theory and recent developments of convex geometric analysis. Firstly, I will explain detailly some related basic concepts and notations in convex geometric analysis. Secondly, I will introduce some useful methods we usually used. Thirdly, I will talk about some hot topics in convex geometric analysis recently and some outstanding research works.