The initial purposes of this 1983 text were to develop mathematical
topics relevant to the study of the incidence and symmetry structures of
geometrical objects and to expand the reader's geometric intuition. The
two fundamental mathematical topics employed in this endeavor are graph
theory and the theory of transformation groups. Part I, Incidence,
starts with two sections on the basics of graph theory and continues
with a variety of specific applications of graph theory. Following this,
the text becomes more theoretical; here graph theory is used to study
surfaces other than the plane and the sphere. Part II, Symmetry, starts
with a section on rigid motions or symmetries of the plane, which is
followed by another on the classification of planar patterns.
Additionally, an overview of symmetry in three-dimensional space is
provided, along with a reconciliation of graph theory and group theory
in a study of enumeration problems in geometry.