1 Introduction  
1.1 Notation and Terminology  
2 The non-degenerate case  
3 The degenerate case  
3.1 Matchings  
3.2 Stars  
3.3 Paths and Cycles  
3.4 Trees  
3.5 Graphs with crosscuts of size two  
3.6 Complete bipartite graphs  
4 Proof Methods  
4.1 Full subgraphs  
4.2 Kővári-Sós-Turán Theorem  
4.3 Delta-systems  
4.4 Ramsey theory, shadows and random sampling  
5 Proof of Theorems  
5.1 Proof of Theorem 3.12  
5.2 Proof of Theorem 3.10 for \(r\geq4\)  
5.3 Proof of Theorems 3.8, 3.10 and 3.11 for \(r=3\)  
6 Open problems