Probability on Graphs - Random Processes on Graphs and Lattices (Broché)

"[Geoffrey Grimmett's book] serves admirably for this "getting started" purpose. It provides a rigorous introduction to a broad range of topics centred on the percolation [interacting particle systems] field... This book, like a typical Part III course, requires only undergraduate background knowledge but assumes a higher level of general mathematical sophistication. It also requires active engagement by the reader.
As I often tell students, "Mathematics is not a spectator sport - you learn by actually doing the exercises !" For the reader who is willing to engage with the material and is not fazed by the fact that some proofs are only outlined or are omitted, this style enables the author to cover a lot of ground." - David Aldous, Bulletin of the American Mathematical Society. "It is written in a condensed style with only the briefest of introductions or motivations, but it is a mine of information for those who are well prepared and know how to use it.
It formed the basis for a Probability reading group at the University of Warwick last term and was well received, and parts of it are being used by a colleague for an undergraduate module this term on Probability and Discrete Mathematics." - RS. MacKay, Contemporary Physics.