This book offers an account of the classical theory of quadratic residues and non-residues with
the goal of using that theory as a lens through which to view the development of some of the
fundamental methods employed in modern elementary algebraic and analytic number theory.The
first three chapters present some basic facts and the history of quadratic residues and
non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth with an
emphasis on the six proofs that Gauss published. The remaining seven chapters explore some
interesting applications of the Law of Quadratic Reciprocity prove some results concerning the
distribution and arithmetic structure of quadratic residues and non-residues provide a
detailed proof of Dirichlet's Class-Number Formula and discuss the question of whether
quadratic residues are randomly distributed. The text is a valuable resource for graduate and
advanced undergraduate students as well as for mathematicians interested in number theory.