Percolation beyond Z d, many questions and a few answers

A comprehensive study of percolation in a more general context than the usual Zd setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results concerning uniqueness of infinite clusters and inequalities for the critical value pc are given, and a simple planar example exhibiting uniqueness and non-uniqueness for different p > pc is analyzed. Numerous varied conjectures and problems are proposed, with the hope of setting goals for future research in percolation theory.