It is four years since the first version of this book appeared and there has continued to be intense activity focused on Lévy processes and related areas. One way of gauging this is to look at the number of books and monographs which have appeared in this time. Regarding fluctuation theory of Lévy processes, there is a new volume by A. Kyprianou and the St Flour lectures of R. Doney. From the point of view of interactions with analysis, N. Jacob has published the third and final volume of his impressive trilogy. Applications to finance has continued to be a highly active and fast moving area and there are two new books here – a highly comprehensive and thorough guide by R. Cont and P. Tankov and a helpful introduction aimed at practioners from W. Schoutens. There have also been new editions of classic texts by Jacod and Shiryaev and Protter.

Changes to the present volume are of two types. On the one hand there was the need to correct errors and typos and also to make improvements where this was appropriate. In this respect, I am extremely grateful to all those readers who contacted me with remarks and suggestions. In particular I would like to thank Fangjun Xu, who is currently a first-year graduate student at Nanzai University, who worked through the whole book with great zeal and provided me with an extremely helpful list of typos and mistakes.