A Comparative Review of Recent Researches in Geometry (Programme on Entering The Philosophical Faculty and The Senate of The University of Erlangen in 1872.)

GROUPS OF SPACE-TRANSFORMATIONS. PRINCIPAL GROUP. FORMULATION OF A GENERAL PROBLEM. GROUPS OF TRANSFORMATIONS, ONE OF WHICH INCLUDES THE OTHER, ARE SUCCESSIVELY ADJOINED. THE DIFFERENT TYPES OF GEOMETRICAL INVESTIGATION AND THEIR RELATION TO EACH OTHER. PROJECTIVE GEOMETRY. TRANSFER OF PROPERTIES BY REPRESENTATIOINS (ABBILDUNG). ON THE ARBITRARINESS IN THE CHOICE OF THE SPACE-ELEMENT. HESSE'S PRINCIPLE OF TRANSFERENCE. LINE GEOMETRY. THE GEOMETRY OF RECIPROCAL RADII. INTERPRETATION OF x+iy. EXTENSION OF THE PRECEDING CONSIDERATIONS. LIE'S SPHERE GEOMETRY. ENUMERATION OF OTHER METHODS BASED ON A GROUP OF POINT-TRANSFORMATIONS. The Group of Rational Transformations. Analysis situs. The Group of all Point-transformations. ON THE GROUP OF ALL CONTACT-TRANSFORMATIONS. ON MANIFOLDNESSES OF ANY NUMBER OF DIMENSIONS. The Projective Method or Modern Algebra (Theory of Invariants). The Manifoldness of Constant Curvature. The Plane Manifoldness.