Shifts of finite type (SFT) and Cuntz-Krieger (CK) algebras are important building blocks in symbolic dynamics and C∗-algebras, respectively. The historic classification interplays between these two different disciplines, dubbed “internal classifications” for C∗-algebras by some experts, continue to inspire today. This tutorial talk is for a general audience in mathematics. In Part I, we will introduce related basics of symbolic dynamics and C∗-algebras, including some key invariants, such as the Bowen-Franks groups of SFT and the K-theory of the CK-algebras. What is common to SFT, CK-algebras and Combinatorics? Finite graphs!