Granville A. An Introduction to Gauss's Number Theory

Montreal: McGill University, 2013. - 363p.We present a modern introduction to number theory, aimed both at students who have little experience of university level mathematics, as well as those who are completing an undergraduate degree. Like most introductions to number theory, our contents are largely inspired by Gauss’s Disquisitiones Arithmeticae (1801), though we also include many modern developments. We have gone back to Gauss to borrow several excellent
examples to highlight the theory.
There are many different topics that might be included in an introductory course in number theory, and others, like the law of quadratic reciprocity, that surely must appear in any such course. We therefore present a “basic” course as the first dozen chapters of the book.