  In this note, we define the Burnside ring of a monoid, generalizing the
construction for groups. After giving foundational definitions, we characterize
transitive M-sets and their automorphisms, then prove a structure theorem for a
broad class of monoids that allows us to write the Burnside ring as a direct
product of Burnside rings of groups. Finally, we define a monoid correlate of
the table of marks, and show that the Burnside algebra over the rationals is
semisimple.
