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Part I History The Revolution of JAnos Bolyai 3 Andrds Prekopa Gauss and non-Euclidean geometry 61 Jeremy Gray JAnos Bolyai's new face 81 Elemdr Kiss Part II Axiomatical and Logical Aspects Hyperbolic Geometry, Dimension-Free 97 Walter Benz An Absolute Property of Four Mutually Tangent Circles 109 H.S.M. Coxeter Remembering Donald Coxeter 115 Asia Ivic Weiss, William Weiss Axiomatizations of hyperbolic and absolute geometries 119 Victor Pambuccian Logical axiomatizations of space-time. Samples from the literature 155 Hajnal Andr6ka, Judit X. Madardsz and Istvdn Nemeti Part III Polyhedra, Volumes, Discrete Arrangements, Fractals Structures in Hyperbolic Space 189 Robert Connelly The Symmetry of Optimally Dense Packings 197 Charles Radin Flexible Octahedra in the Hyperbolic Space 209 Hellmuth Stachel Fractal Geometry On Hyperbolic Manifolds 227 Bernd O. Stratmann A volume formula for generalised hyperbolic tetrahedra 249 Akira Ushijima Part IV Tilings, Orbifolds and Manifolds, Visualization The Geometry of Hyperbolic Manifolds of Dimension at least 4 269 John G. Ratcliffe Real-Time Animation in Hyperbolic, Spherical, and Product Geometries 287 Jeffrey R. Weeks On spontaneous surgery on knots and links 307 A.D. Mednykh, V.S. Petrov Classification of tile-transitive 3-simplex tilings and their realizations 321 E. Molndr - I. Prok - J. Szirmai Part V Differential Geometry Non-Euclidean Analysis 367 Sigurdur Helgason Holonomy, geometry and topology of manifolds with Grassmann structure 385 Neda Bokan, Paola Matzeu, Zoran Rakid Hypersurfaces of type number 2 in the hyperbolic four-space 407 Oldhich Kowalski, Masami Sekizawa How far does hyperbolic geometry generalize? 427 Jdnos Szenthe Geometry of the point Finsler spaces 445 Lajos Tamdssy Part VI Physics Black hole perturbations 465 Zoltdn Perjes An Idea Whose Time Has Returned 487 Abraham A. Ungar