Title: Zero sets of real polynomials Abstract: Stein conjectured that the Fourier extension operator is bounded between certain $L^p$ spaces. Recently people have found that auxiliary real polynomials can help in the study of the above conjecture (usually known as the Restriction Conjecture). We will talk about a few interesting facts about zero sets of real polynomials, on their proofs, and a bit on why they can be useful in the study of the Restriction Conjecture.