Primary Sources

• Bolyai, J., 1832. Scientia absoluta spatii. Appendix to Bolyai, F., Tentamen juventutem studiosam in elementa matheseos purae elementis ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi, Tomus Primus. Maros Vasarhely: J. et S. Kali. (English translation by G. B. Halsted printed as a supplement to Bonola 1955.) (Scholar)
• Cayley, Arthur, 1859. “A sixth memoir upon quantics,” Philosophical Transactions of the Royal Society of London, 149: 61–90.
• Ehresmann, Ch., 1957. “Les connexions infinitésimales dans un espace fibré différentiable,” in Colloque de Topologie (Espaces Fibrés), Bruxelles 1950, Paris: Masson, pp. 29–55. (Scholar)
• Einstein, A., 1915. “Die Feldgleichungen der Gravitation,” Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1915), pp. 844–847. (Scholar)
• Einstein, A., 1916. “Die Grundlagen der allgemeinen Relativitätstheorie,” Annalen der Physik, 49: 769–822. (Scholar)
• Euclides, Elementa, I. L. Heiberg (ed.), Leipzig: B. G. Teubner, 5 volumes., 1883–88. (For English translation, see below under Heath). (Scholar)
• Gauss, C. F., 1828. Disquisitiones generales circa superficies curvas, Göttingen: Dieterich. (English translation by A. Hiltebietel and J. Morehead: Hewlett, NY, Raven Press, 1965.) (Scholar)
• Hilbert, D., 1899. “Die Grundlagen der Geometrie,” in Festschrift zur Feier der Enthüllung des Gauss-Weber Denkmals, Leipzig: B.G. Teubner, pp. 3–92. (Scholar)
• Hilbert, D., 1968. Grundlagen der Geometrie, mit Supplementen von P. Bernays. Zehnte Auflage. Stuttgart: Teubner. (Tenth, revised edition of Hilbert 1899.) (Scholar)
• Klein, F., 1871. “Über die sogenannte Nicht-Euklidische Geometrie,” Mathematische Annalen, 4: 573–625. (Scholar)
• Klein, F., 1872. Vergleichende Betrachtungen über neuere geometrische Forschungen, Erlangen: A. Duchert. (Scholar)
• Klein, F., 1873. “Über die sogenannte Nicht-Euklidische Geometrie (Zweiter Aufsatz),” Mathematische Annalen, 6: 112–145. (Scholar)
• Klein, F., 1893. “Vergleichende Betrachtungen über neuere geometrische Forschungen,” Mathematische Annalen, 43: 63–100. (Revised version of Klein 1872). (Scholar)
• Klein, F., 1911. “Über die geometrischen Grundlagen der Lorentz-Gruppe,” Physikalische Zeitschrift, 12: 17–27. (Scholar)
• Lie, S., 1888–1893. Theorie der Transformationsgruppen (3 volumes), Unter Mitwirkung von F. Engel, Leipzig: Teubner. (Scholar)
• Lobachevsky, N. I., 1837. “Géométrie imaginaire,” Journal für die reine und angewandte Mathematik, 17: 295–320.
• Lobachevsky, N. I., 1840. Geometrische Untersuchungen zur Theorie der Parallellinien, Berlin: F. Fincke. (English translation by G. B. Halsted printed as a supplement to Bonola 1955.) (Scholar)
• Lobachevsky, N. I., 1856. Pangéométrie ou précis de géométrie fondée sur une théorie générale et rigoureuse des parallèles, Kazan: Universitet. (Scholar)
• Locke, J., 1690. An Essay concerning Humane Understanding (in four books), London: Printed for Thomas Basset and sold by Edward Mory. (Published anonymously; the author's name was added in the second edition). (Scholar)
• Minkowski, H., 1909. “Raum und Zeit,” Physikalische Zeitschrift, 10: 104–111. (Scholar)
• Pasch, M., 1882. Vorlesungen über neueren Geometrie, Leipzig: Teubner. (Scholar)
• Poincaré, H., 1887. “Sur les hipothèses fondamentales de la géométrie,” Bulletin de la Société mathématique de France, 15: 203–216. (Scholar)
• Poncelet, J. V., 1822. Traité des propriétés projectives des figures, Paris: Bachelier. (Scholar)
• Ricci, G. and T. Levi-Cività, 1901. “Méthodes de calcul différentiel absolu et leurs applications,” Mathematische Annalen, 54: 125–201.
• Riemann, B., 1854. “Über die Hypothesen, welche der Geometrie zugrunde liegen,” Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 13 (1867): 133–152. (For English translation, see below under Spivak.) (Scholar)
• Riemann, B., 1861. “Commentatio mathematica, qua respondere tentatur quaestioni ab illustrissima Acad. Parisiensi propositae,” in Bernhard Riemanns gesammelte mathematische Werke und wissenschaftlicher Nachlass, Leipzig: Teubner, 1876, pp. 391–404. (Scholar)
• Russell, B., 1897. An Essay on the Foundations of Geometry, Cambridge: Cambridge University Press. (Unaltered reprint: New York, Dover, 1956.) (Scholar)
• Saccheri, G. 1733. Euclides ab omni nævo vindicatus sive conatus geometricus quo stabiliuntur prima ipsa universæ geometriæ principia, Mediolani: Ex Typographia Pauli Antonii Montani. (Reprint, with facing English translation by G. B. Halsted: New York, Chelsea, 1986.) (Scholar)

Secondary Literature

• Acuña, Pablo, 2016. “Minkowski spacetime and Lorentz invariance: The cart and the horse or two sides of a single coin?,” Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 55: 1–12. (Scholar)
• Blumenthal, L. M., 1961. A Modern View of Geometry, San Francisco: Freeman. (Scholar)
• Boi, Luciano, 1995. Le problème mathématique de l'espace: Une quête de l'intelligible, Berlin: Springer. (Scholar)
• Bonola, R., 1955. Non-Euclidean Geometry: A critical and historical study of its development. English translation with additional appendices by H.S. Carslaw. New York: Dover. (Scholar)
• Freudenthal, H., 1957. “Zur Geschichte der Grundlagen der Geometrie,” Nieuw Archief vor Wiskunde, 5: 105–142. (Scholar)
• Freudenthal, H., 1960. “Die Grundlagen der Geometrie um die Wende des 19. Jahrhunderts,” Mathematisch-physikalische Semesterbericht, 7: 2–25. (Scholar)
• Gallot, S., D. Hulin, and J. Lafontaine, 2004. Riemannian Geometry, Berlin: Springer, 3rd edition. (An up-to-date textbook, with solutions to odd-numbered exercises. A section is devoted to the “pseudo”-Riemannian geometry employed in Relativity Theory.) (Scholar)
• Giedymin, J., 1982. Science and Convention: Essays on Henri Poincaré's Philosophy of Science and the Conventionalist Tradition, Oxford: Pergamon. (Scholar)
• Greenberg, M. J., 2008. Euclidean & Non-Euclidean Geometry: Development and History, New York: Freeman, 4th edition. (An excellent tool for self-study at the high-school senior or college freshman level.) (Scholar)
• Heath, T. L., 1956. The Thirteen Books of Euclid's Elements, translated from the text of Heiberg with introduction and commentary, New York: Dover, 3 volumes, 2nd edition, revised with additions. (Scholar)
• Magnani, L., 2001. Philosophy and Geometry: Theoretical and Historical Issues, Dordrecht: Kluwer. (Scholar)
• Nagel, E., 1939. “The formation of modern conceptions of formal logic in the development of geometry,” Osiris, 7: 142–224. (Scholar)
• O'Neill, B., 1983. Semi-Riemannian Geometry with Applications to Relativity, New York: Academic Press. (Scholar)
• Nomizu, K., 1956. Lie Groups and Differential Geometry, Tokyo: The Mathematical Society of Japan. (Scholar)
• Ronan, M., 2008. “Lie Theory,” in T. Gowers (ed.), The Princeton Companion to Mathematics, Princeton, NJ: Princeton University Press, pp. 229–234. (Scholar)
• Rosenfeld, B. A., 1988. A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, translated by Abe Shenitzer, New York: Springer. (Scholar)
• Spivak, M., 1979. A Comprehensive Introduction to Differential Geometry (5 volumes), Berkeley: Publish or Perish, 2nd edition. (Contains an excellent English translation, with mathematical commentary, of Riemann's lecture “On the hypotheses that lie at the foundation of geometry”; see Vol. 2, pp. 135ff.) (Scholar)
• Torretti, R., 1978. Philosophy of Geometry from Riemann to Poincaré, Dordrecht: Reidel. (Corrected reprint: Dordrecht, Reidel, 1984). (Scholar)
• Trudeau, R. J., 1987. The Non-Euclidean Revolution, Boston: Birkhäuser. (Scholar)
• Winnie, J. W., 1986. “Invariants and objectivity: A theory with applications to relativity and geometry,” in R. G. Colodny (ed.), From Quarks to Quasars, Pittsburgh: Pittsburgh University Press, pp. 71–180. (Scholar)