I. Curves in Space
II. Curvilinear Coordinates on a Surface. Envelopes
III. Linear Element of a Surface. Differential Parameters. Conformal Representation
IV. Geometry of a Surface in the Neighborhood of a Point
V. Fundamental Equations. The Moving Trihedral
VI. Systems of Curves. Geodesics
VII. Quadrics. Ruled Surfaces. Minimal Surfaces
VIII. Surfaces of Constant Total Curvature. W-Surfaces. Surfaces with Plane or Spherical Lines of Curvature
IX. Deformation of Surfaces
X. Deformation of Surfaces. The Method of Weingarten
XI. Infinitesimal Deformation of Surfaces
XII. Rectilinear Congruences
XIII. Cyclic Systems
XIV. Triply Orthogonal Systems of Surfaces
Index

Created especially for graduate students, this introductory treatise on differential geometry has been a highly successful textbook for many years. Its unusually detailed and concrete approach includes a thorough explanation of the geometry of curves and surfaces, concentrating on problems that will be most helpful to students. 1909 edition.