In Moscow I gave 4+1 lectures where 4 lecture were kind of introductions to Extremal Graph Theory, and these NOTES are reminders but do not follow the actual lectures.
The following early survey explaines many details:
Extremal Graph Theory from "Selected topics in ... (eds Beineke and Wilson)
This huge file will be replaced by a much more concise "annotated" one, which also contains many extra remarks, references and figures.
One can find a detailed survey of Komlos and Simonovits on this topic in:
Komlós, J. and Simonovits, M.: Szemerédi's regularity lemma and its applications in graph theory. Combinatorics, Paul
Erdös is eighty, Vol. 2 (Keszthely, 1993), 295--352, Bolyai Soc. Math. Stud., 2, János Bolyai Math. Soc., Budapest, 1996.
The following is a continuation of the Komlos-Simonovits survey, a little more technical, but very informative.
Komlós, János; Shokoufandeh, Ali; Simonovits, Miklós and Szemerédi, Endre: The regularity lemma and its
applications in graph theory. Theoretical aspects of computer science (Tehran, 2000), 84--112, Lecture Notes in Comput. Sci., 2292,
Springer, Berlin, 2002. [pdf]
Some further subareas:
One can find a detailed survey of Furedi and Simonovits on this topic in:
Füredi, Zoltán and Simonovits, Miklós: The history of
degenerate (bipartite extremal graph problems). Erdös centennial, 169--264, Bolyai Soc. Math. Stud., 25, János Bolyai
Math. Soc., Budapest, 2013. [pdf]
The following topics will be treated later
actually, they are described in the surveys above