| Preface to the third edition | p. xi |
| Preface to the first edition | p. xiii |
| List of notation | p. xvii |
| Introduction | p. 1 |
| Graphs | p. 9 |
| Abstract graphs and realizations | p. 9 |
| Kirchhoff's laws | p. 14 |
| Maximal trees and the cyclomatic number | p. 16 |
| Chains and cycles on an oriented graph | p. 20 |
| Planar graphs | p. 26 |
| Appendix on Kirchhoff's equations | p. 35 |
| Closed surfaces | p. 38 |
| Closed surfaces and orientability | p. 39 |
| Polygonal representation of a closed surface | p. 45 |
| A note on realizations | p. 47 |
| Transformation of closed surfaces to standard form | p. 49 |
| Euler characteristics | p. 55 |
| Minimal triangulations | p. 60 |
| Simplicial complexes | p. 67 |
| Simplexes | p. 67 |
| Ordered simplexes and oriented simplexes | p. 73 |
| Simplicial complexes | p. 74 |
| Abstract simplicial complexes and realizations | p. 77 |
| Triangulations and diagrams of simplicial complexes | p. 79 |
| Stars, joins and links | p. 84 |
| Collapsing | p. 88 |
| Appendix on orientation | p. 93 |
| Homology groups | p. 99 |
| Chain groups and boundary homomorphisms | p. 99 |
| Homology groups | p. 104 |
| Relative homology groups | p. 112 |
| Three homomorphisms | p. 121 |
| Appendix on chain complexes | p. 124 |
| The question of invariance | p. 127 |
| Invariance under stellar subdivision | p. 128 |
| Triangulations, simplicial approximation and topological invariance | p. 133 |
| Appendix on barycentric subdivision | p. 136 |
| Some general theorems | p. 138 |
| The homology sequence of a pair | p. 138 |
| The excision theorem | p. 142 |
| Collapsing revisited | p. 144 |
| Homology groups of closed surfaces | p. 149 |
| The Euler characteristic | p. 154 |
| Two more general theorems | p. 158 |
| The Mayer-Vietoris sequence | p. 158 |
| Homology sequence of a triple | p. 167 |
| Homology modulo 2 | p. 171 |
| Graphs in surfaces | p. 180 |
| Regular neighbourhoods | p. 183 |
| Surfaces | p. 187 |
| Lefschetz duality | p. 191 |
| A three-dimensional situation | p. 195 |
| Separating surfaces by graphs | p. 198 |
| Representation of homology elements by simple closed polygons | p. 200 |
| Orientation preserving and reversing loops | p. 203 |
| A generalization of Euler's formula | p. 207 |
| Brussels Sprouts | p. 211 |
| Appendix: abelian groups | p. 215 |
| Basic definitions | p. 215 |
| Finitely generated (f.g.) and free abelian groups | p. 217 |
| Quotient groups | p. 219 |
| Exact sequences | p. 221 |
| Direct sums and splitting | p. 222 |
| Presentations | p. 226 |
| Rank of a f.g. abelian group | p. 233 |
| References | p. 239 |
| Index | p. 243 |
| Table of Contents provided by Ingram. All Rights Reserved. |