This conference is a celebration of Prof. Tony Guttmann’s 70th birthday, an acknowledgment of his enormous contribution to Mathematics in Australia and of his field of research: Critical Phenomena in Statistical Mechanics. Amongst Prof. Guttmann many contributions to Australian Mathematics was his initial contribution to the founding of AMSI. Attending this conference are several international and national leaders in the field of Critical Phenomena, Enumerative Combinatorics, Algebraic Combinatorics and Computational Algorithms. These are fields of mathematics that all play a signification part in the mathematical understanding of Critical Phenomena.