Main text: N. Alon, J. Spencer: The Probabilistic Method (Fourth edition, Wiley, 2016)
Further reading: B. Bollobas, Random Graphs, (Second Edition, Cambridge University Press, 2001)
S. Janson, T. Luczak and A. Rucinski, Random Graphs, (Wiley, 2000)
M. Molloy and B. Reed, Graph Colouring and the Probabilistic Method, (Springer, 2002)