The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently. It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to advanced students and researchers. Basic concepts - Introduction to Graph Theory - Trees and electrical networks - Matroids - Geometric representations of graphs - Game of dualities - The zeta function and graph polynomials - Knots - 2D Ising and dimer models - Advanced Graduate Students in Mathematics, Physics and Computer Sciences - Researchers Prof. Dr. Martin Loebl, Dept. of Mathematics, Charles University, Prague.