  The Law of Quadratic Reciprocity was conjectured by Euler and Legendre who
both found an incomplete proof. Gauss called this law "Theorema Fundamentale",
and he was the first who gave a complete proof, he also highlighted the
equivalence of his formulation with those of Euler and Legrendre. Hereby notes
gives a overview of the Theory of Quadratic Residues using a classical approach
with some application to Diophantine Equations, such as Two Square Theorem and
Pythagorean Quadruplets.
