This book is loosely based on lecture notes entitled An introduction to finite geometry that Zsuzsa Weiner and I wrote, and I would like to thank Zsuzsa for her collaboration on that project. Those notes themselves were inspired by Peter Cameron's notes entitled Projective and polar spaces, so I also thank Peter for his notes and for giving freely his time and expertise over the years. The chapters on the forbidden subgraph problem and MDS codes are based on lecture notes I wrote for the CIMPA Graphs, Codes and Designs summer school held in May 2013 at Ramkhamhaeng University, Bangkok, Thailand. I would like to thank all those connected with the school, especially Somporn Sutinuntopas for organising and coordinating the event.

I would like to thank Mark Ioppolo, who read the text of this book in its earlier stages, for his comments and his general enthusiasm for the project. I would like to thank Frank De Clerck for his corrections and comments regarding the first four chapters of the text. I would like to thank Ameerah Chowdhury for her comments on the chapter on MDS codes. I would like thank Tim Alderson and Aart Blokhuis for their suggestions related to the chapter on Combinatorial applications.

The figures in this book were made using GeoGebra, which I found to be an easy-to-use and useful package. (http://www.geogebra.org)

Fields

The book by Lidl & Niederreiter (1997) is a comprehensive text dedicated to finite fields. The recent book by Mullen (2013) contains a wealth of results concerning finite fields and their applications.

For a more general view of the algebraic objects mentioned here, see Lang (1965).

For a survey on finite semifields (albeit not up-to-date), see Kantor (2006).