  This is an unrefereed lecture note based on lectures in 'Introductory
Workshop on Discrete Differential Geometry' at Korea University on January
21--24, 2019. In this note, we discuss topological crystallography, which is a
mathematical theory of crystal structures. The most symmetric structure among
all placements of the graph is obtained by a variational principle in
topological crystallography. We also discuss a theory of trivalent discrete
surfaces in $3$-dimensional Euclidean space, which are mathematical models of
crystal/molecular structures.
