Includes appendix and index

Introduction -- Basic number theory -- Integral solutions to the Pythagorean Equation -- What integers are areas of right triangles? -- What numbers are the edges of a right triangle? -- Primes of the form 4k+1 -- Gauss sums, Quadratic Reciprocity, and the Jacobi symbol -- Advanced Topics -- Counting Pythagorean triples modulo an integer -- How many lattice points are there on a circle or a sphere? -- What about geometry? -- Another proof of the four squares theorem -- Quadratic forms and sums of squares -- How many Pythagorean triples are there? -- How are rational points distributed, really?