List of a few key errata: There is a missing squared in the proof of 3.7.1. Try to find it. Proposition 5.2.4, proof, should have "nd | (ad-bd)" instead of "ad-bd | nd". Thanks to Phillip Poplin for noticing. The proof of 12.4.2 has an error in the last line, which should start 2^{[(2^n-1)-1]/2}; thanks to George Jennings. Fact 14.2.1 is exactly opposite the truth, I believe. The formula Hilbert-Waring in 14.2.8 should have 2^m+floor((3/2)^m)-2; the exponent inside the floor is missing. The explanation of Figure 16.3.5 is for Lagrange's Table IV, not Table III. The statement of Theorem 19.2.5 has an obvious typo of e^i instead of e_i in the formula for \sigma_0 . I know there are some in exercises but I have not collated them into a single document.