1 Introduction  
2 Preliminaries  
2.1 Definitions of Graph Algebras  
2.2 Computation of $K$-groups  
3 Classification of Simple and Nonsimple Graph $C^{*}$-algebras  
4 In Search of Techniques to Classify Algebras: Shift Spaces, Flow Equivalence, and Moves on Graphs  
5 Classification of Leavitt Path Algebras of Finite Graphs  
6 Classification of Leavitt Path Algebras of Infinite Graphs