famous graduate-level treatise in mathematics: A Course in Arithmetic, by J.-P. Serre

Here is the link to an online pdf version of the text.

keywords:

[quadratic reciprocity]

[classification of quadratic forms over the field of rational numbers]

[purely algebraic]

[analytic methods]

[Hasse-Minkowski theorem]

[p-adic fields]

[Hilbert symbols]