Differential geometry has become one of the most active areas of math publishing, yet a small list of older, unofficial classics continues to interest the contemporary generation of mathematicians and students. This advanced treatment of topics in differential geometry, first published in 1957, was praised as "well written" by The American Mathematical Monthly and hailed as "undoubtedly a valuable addition to the literature." Its topics include: - Spaces with a non-vanishing curvature tensor that admit a group of automorphisms of the maximum order - Groups of transformations in generalized spaces - The study of global properties of the groups of motions in a compact orientable Riemannian space - Lie derivatives in an almost complex space For advanced undergraduates and graduate students in mathematics