Béla Bollobás has been a fellow at Trinity College, Cambridge, for over 55 years, for decades as Director of Studies in Mathematics, and is the Chair of Excellence in Combinatorics at the University of Memphis. He has supervised over 70 PhD students. He is a fellow of the Royal Society, a foreign member of the Hungarian, Polish and Brazilian Academies of Sciences. Among the awards he has received are the Senior Whitehead Prize, the Széchenyi Prize, an Honorary Doctorate from Adam Mickiewicz University, Poznań, and the Commander's Cross of the Hungarian Order of Merit. This is his 14th book. Robert Morris has taught graph theory and combinatorics at IMPA, Rio de Janeiro, for the past 15 years and has had more than 20 PhD and Master's students. He is a member of the Brazilian Academy of Sciences and has been awarded numerous prizes, including the European Prize in Combinatorics, the Fulkerson Prize, the MCA Prize, and the Leroy P. Steele Prize for Seminal Contribution to Research. His first book was awarded the Elon Lages Lima Prize by the Brazilian Mathematical Society. This is his second book.

• Introduction; 1. Basic graph theory; 2. Extremal graph theory; 3. Classical graph theory; 4. Ramsey theory; 5. Random graphs.

'This book is a beautiful tour through graph theory. The book starts gently and carefully guides readers through the essential topics in the area, providing intuition and motivation at each step, before setting the reader up for more advanced topics. The pacing is ideal for a first course in graph theory and additionally contains many excellent exercises.' Julian Sahasrabudhe, University of Cambridge