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In recent years we have seen great breakthroughs in the classification theory of higher dimensional compact algebraic varieties and complex manifolds. The seminal results are the proofs of finite generations of canonical rings of algebraic varieties by Caucher Birkar - Paolo Cascini - Christopher D. Hacon - James McKernan [BCHM06] using the algebraic method and Yum-Tong Siu [Siu08] using the analytic method. These results have profound influence on many areas of mathematics - including the study of higher dimensional dynamics and number theoretical dynamics. The interactions of algebraic geometry and the study of these dynamics is exactly the main theme of this program.