Abstract: The research of coloring graphs on surfaces originated
from Heawood map color theorem. With an analysis based on the
primary source, we survey the work of Thomassen, such as three color
theorem and list coloring, coloring graphs on surfaces, and
chromatic polynomial and number of colorings. His work
 has been concerned by many mathematicians, such as Mohar, Thomas and Hutchinson.

Key words: surface, embedded graph, coloring, chromatic polynomial