Page 40: ℚ[√-N] should be ℚ(√-N).

Page 77: The two occurences of (log log N)^-1/2 on this page should be (log log N)^1/2.

Page 98: In the middle of the page, the expression "G(2/u,1/u)" should read "G(1/u,2/u)".

Page 132: In line 2, the expression "p lcm(p-1,p²-1)" on the RHS should be followed by "= p³-p" (this is not an error, just a bit strange as written).

Page 132: In the statement of Proposition 8.4, "...divides a random element..." should be replaced with "...divides the order of a random element...".
The same comment applies to footnote 2 at the bottom of the page 132.

Pages 139 and 185: To avoid possible confusion, the symbol "⊗" should be replaced by "×" everywhere it appears on the page. No tensor products are involved.

Pages 154, 155, 160, 162, 185: ℚ[√D] should be ℚ(√D) everywhere it appears.

Pages 182, 183, 184, 202, and 204: In tables A.1, A.2, A.3, B.16, and B.18 the first column should be labeled n, not D.

Page 210: The bibliographic entry for Shanks has the wrong first name, it should read "Daniel Shanks".