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 If A is a pointed abelian monoid, its prime ideals make sense and form a topological space, analogous to Spec of a ring; the notion of a monoid scheme is analogous to the notion of a scheme in Algebraic Geometry. The monoid ring construction k[A] gives a link to geometry. In this talk I will give an introduction to the basic ideas, including toric monoid schemes, which model toric varieties.