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In this self-contained textbook, algebraic graph theory is used to introduce groups; topologicalgraph theory is used to explore surfaces; and geometric graph theory is implemented to analyse incidence geometries. It includes 200 illustrations, exercises and open problems.

This book presents rigidity theory in a historical context. The combinatorial aspects of rigidity are isolated and framed in terms of a special class of matroids, which are a natural generalization of the connectivity matroid of a graph. The book includes an introduction to matroid theory and an extensive study of planar rigidity. The final chapter is devoted to higher dimensional rigidity, highlighting the main open questions. Also included is an extensive annotated bibiolography with over 150 entries. The book is aimed at graduate students and researchers in graph theory and combinatorics...