This book is about the mathematics of percolation theory，withthe emphasis upon presenting the shortest rigorous proofs of themain facts.I have made certain sacrifices in order to maximize theaccessibility of the theory，and the major one has been to restrictmyself almost entirely to the special case of bond percolation onthe cubic lattice Zd.Thus there is only little discussion of suchprocesses as continuum，mixed，inhomogeneous，long-range，first-passage，and oriented percolation.Nor have I spent much timeor space on the relationship of percolation to statisticalphysics，infinite particle systems，disordered media，reliabilitytheory，and so on.With the exception of the two final chapters，Ihave tried to stay reasonably close to core material of the sortwhich most graduate students in the area might aspire to know.Nocritical reader will agree entirely with my selection，andphysicists may sometimes feel that my intuition is crooked.