| Foreword | p. xi |
| Prefatory note | p. xxiii |
| Kummer's Configuration | |
| Desmic tetrahedra | p. 1 |
| The group of reflexions | p. 4 |
| The 16[subscript 6] configuration | p. 5 |
| The group of sixteen operations | p. 6 |
| The incidence diagram | p. 7 |
| Linear construction from six arbitrary planes | p. 8 |
| Situation of coplanar points | p. 12 |
| The Quartic Surface | |
| The Quartic surface with sixteen nodes | p. 14 |
| Nomenclature for the nodes and tropes | p. 16 |
| The equation of the surface | p. 17 |
| The shape of the surface | p. 19 |
| The Orthogonal Matrix Of Linear Forms | |
| Preliminary account of matrices | p. 24 |
| Orthogonal matrices | p. 26 |
| Connection between matrices and quaternions | p. 27 |
| The sixteen linear forms | p. 28 |
| Quadratic relations | p. 30 |
| The ten fundamental quadrics | p. 32 |
| The six fundamental complexes | p. 33 |
| Irrational equations of Kummer's surface | p. 34 |
| Line Geometry | |
| Polar lines | p. 37 |
| Apolar complexes | p. 38 |
| Groups of three and four apolar complexes | p. 39 |
| Six apolar complexes | p. 40 |
| Ten fundamental quadrics | p. 41 |
| Klein's 60[subscript 15] configuration | p. 42 |
| Kummer's 16[subscript 6] configuration | p. 44 |
| Line coordinates | p. 45 |
| Fundamental quadrics | p. 47 |
| Fundamental tetrahedra | p. 48 |
| The Quadratic Complex And Congruence | |
| Outline of the geometrical theory | p. 50 |
| Outline of the algebraical theory | p. 53 |
| Elliptic coordinates | p. 55 |
| Conjugate sets | p. 56 |
| Klein's tetrahedra | p. 57 |
| Relations of lines to [Phi] | p. 58 |
| Asymptotic curves | p. 60 |
| Principal asymptotic curves | p. 62 |
| The congruence of second order and class | p. 63 |
| Singularities of the congruence | p. 63 |
| Relation between [Phi] and [Lambda] | p. 65 |
| Confocal congruences | p. 66 |
| Plucker's Complex Surface | |
| Tetrahedral complexes | p. 68 |
| Equations of the complex and the complex surface | p. 69 |
| Singularities of the surface | p. 71 |
| The polar line | p. 72 |
| Shape of the surface | p. 73 |
| Sets Of Nodes | |
| Group-sets | p. 75 |
| Comparison of notations | p. 76 |
| Pairs and octads | p. 77 |
| Eighty Rosenhain odd tetrads | p. 78 |
| Sixty Gopel even tetrads | p. 79 |
| Odd and even hexads | p. 80 |
| Equations Of Kummer's Surface | |
| The equation referred to a fundamental tetrahedron | p. 81 |
| The equation referred to a Rosenhain tetrahedron | p. 83 |
| Nodal quartic surfaces | p. 86 |
| Special Forms Of Kummer's Surface | |
| The tetrahedroid | p. 89 |
| Multiple tetrahedroids | p. 91 |
| Battaglini's harmonic complex | p. 94 |
| Limiting forms | p. 98 |
| The Wave Surface | |
| Definition of the surface | p. 100 |
| Apsidal surfaces | p. 101 |
| Singularities of the Wave Surface | p. 102 |
| Parametric representation | p. 104 |
| Tangent planes | p. 106 |
| The four parameters | p. 108 |
| Curvature | p. 109 |
| Asymptotic lines | p. 110 |
| Painvin's complex | p. 112 |
| Reality And Topology | |
| Reality of the complexes | p. 115 |
| Six real fundamental complexes | p. 118 |
| Equations of surfaces I[subscript a], I[subscript b], I[subscript c] | p. 121 |
| Four real and two imaginary complexes | p. 122 |
| Two real and four imaginary complexes | p. 125 |
| Six imaginary complexes | p. 126 |
| Geometry Of Four Dimensions | |
| Linear manifolds | p. 127 |
| Construction of the 15[subscript 6] configuration from six points in four dimensions | p. 129 |
| Analytical methods | p. 130 |
| The 16[subscript 6] configuration | p. 131 |
| General theory of varieties | p. 132 |
| Space sections of a certain quartic variety | p. 134 |
| Algebraic Curves On The Surface | |
| Geometry on a surface | p. 137 |
| Algebraic curves on Kummer's surface | p. 138 |
| The [Theta]-equation of a curve | p. 141 |
| General theorems on curves | p. 142 |
| Classification of families of curves | p. 145 |
| Linear systems of curves | p. 146 |
| Curves Of Different Orders | |
| Quartic curves | p. 149 |
| Quartics through the same even tetrad | p. 151 |
| Quartics through the same odd tetrad | p. 153 |
| Sextics through six nodes | p. 154 |
| Sextics through ten nodes | p. 157 |
| Octavic curves through eight nodes | p. 158 |
| Octavic curves through sixteen nodes | p. 159 |
| Weddle's Surface | |
| Birational transformation of surfaces | p. 160 |
| Transformation of Kummer's surface | p. 162 |
| Quartic surfaces into which Kummer's surface can be transformed | p. 165 |
| Weddle's surface | p. 166 |
| Equation of Weddle's surface | p. 169 |
| Theta Functions | |
| Uniformisation of the surface | p. 173 |
| Definition of theta functions | p. 175 |
| Characteristics and periods | p. 176 |
| Identical relations among the double theta functions | p. 179 |
| Parametric expression of Kummer's surface | p. 180 |
| Theta functions of higher order | p. 182 |
| Sketch of the transcendental theory | p. 184 |
| Applications Of Abel's Theorem | |
| Tangent sections | p. 188 |
| Collinear points | p. 190 |
| Asymptotic curves | p. 194 |
| Inscribed configurations | p. 196 |
| Singular Kummer Surfaces | |
| Elliptic surfaces | p. 200 |
| Transformation of theta functions | p. 201 |
| The invariant | p. 203 |
| Parametric curves | p. 204 |
| Unicursal curves | p. 206 |
| Geomtrical interpretation of the singular relation k[tau subscript 12]=1 | p. 208 |
| Intermediary functions | p. 210 |
| Singular curves | p. 212 |
| Singular surfaces with invariant 5 | p. 213 |
| Singular surfaces with invariant 8 | p. 214 |
| Birational transformations of Kummer surfaces into themselves | p. 216 |
| Index | p. 221 |
| Plate | |
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