  In this expository paper, we present simple proofs of the Classical, Real,
Projective and Combinatorial Nullstellens\"atze. Several applications are also
presented such as a classical theorem of Stickelberger for solutions of
polynomial equations in terms of eigenvalues of commuting operators,
construction of a principal ideal domain which is not Euclidean, Hilbert's
$17^{th}$ problem, the Borsuk-Ulam theorem in topology and solutions of the
conjectures of Dyson, Erd\"{o}s and Heilbronn.
