This is the first book completely devoted to continuum percolation. The idea to write this book came up after we noticed that even specialists working in the larger area of spatial random processes were unaware about the current state of the art of continuum percolation. Although stochastic geometers have extensively studied the Boolean model, which is one of the most common models of continuum percolation, their focus has been on geometric and statistical aspects rather than on percolation-theoretical issues.

Initially, we planned to write a review article, but it became clear very quickly that it would be impossible to cover even the most basic results in such a review. Also it became apparent that it would be impossible to include in one volume all available results of a subject this size and still expanding. Therefore, we decided on a book which would give attention to all major issues and techniques without necessarily pushing them to the frontier of today's knowledge. When there is more to say on a specific subject than is found here, we provide the appropriate references for further reading.

Continuum percolation models are easily described verbally, but unlike discrete percolation models, their formal mathematical construction is not completely straightforward. In fact, many people (the authors included) have been quite careless with these constructions in the literature. The setup we have chosen in this book is probably the simplest rigorous construction which allows us to use all the ergodic theory we want.