Extremal graph theory and applying the regularity lemma

The main source used in the preparation of this study is Diestel's (2017) "Graph Theory" book. This thesis mainly consists of studying the seventh chapter of the aforementioned book to understand and explain the subject of "extremal graph theory". But of course, no part of the mentioned book has been quoted exactly, a study has been put forward with our own words and our own sentences; and on the one hand, some very difficult or technical proofs were skipped, on the other hand, some parts of the book that were left to the reader were explained and the subject was presented more understandably. In addition to these, the articles listed in the references were also consulted. To summarize in outline: In the first chapter, basic definitions and theorems of graph theory, which are the prerequisites for understanding the main subject, are covered by using the first chapter of the aforementioned book. In the first section of the second chapter, the question of what edge density is required to force a graph to contain a copy of a given graph is sought; and in the second section, the same problem is discussed in terms of inclusion as a minor. In the third section, Hadwiger's (1943) conjecture and related results; and in the fourth section, the Szemeredi lemma of regularity and its proof are studied. In the fifth and the last section of the second chapter, a general method of applying the Szemeredi lemma is introduced and as an example of this method, the theorem of Erdös and Stone (1946) is proved. In the third chapter of the thesis, before the conclusions and recommendation chapter, a brief literature review on the subject of the thesis is presented by using the notes section of the seventh chapter of the mentioned book.