On p239, exercise 5.5.17: I don’t think this example works. The problem is that the midpoints of the quadrilateral , , , themselves form a parallelogram, and this rules out any non-standard Freiman homomorphisms to .

Replacing the generic quadrilateral with a generic pentagon in should fix it, I think, giving a universal ambient group of .

(Also, I think there is a typo

on the penultimate line: the first “2” should be a “4”.)

*[Correction added, thanks – T.]*

On p241, proof of Lemma 5.45, last line of the first displayed equation: I think

should read

as an estimate on the binomial coefficient.

*[Correction added, thanks – T.]*

*[Correction added, thanks – T.]*

*[Correction added, thanks – T.]*

p. 285: Corollary 5.25 should be Lemma 5.25.

*[Correction added, thanks – T.]*

on page 281, last paragraph it says “we can reduce further to the case that $Z$ is odd”, which should probably read “$|Z|$ is odd” or “the order of $Z$ is odd”?

PS: I do not know if it is actually useful to report such minor typos?

*[Correction added, thanks -T.]*

On page 294, after the very first proof (of 7.20), it says “however one can lower dimension its by increasing”, probably instead of “lower its dimension by increasing”.

*[Correction added, thanks – T.]*

*[Correction added, thanks – T.]*

in the final lines of the proof of Freiman’s 3k-3 Theorem (page 208) it appears that the inequality is used reversed, and I can’t see how the relative errata above can fix this. Am I wrong?

*[Gah, the previous erratum was not applied correctly. I’ve now supplied a revised erratum in the second errata list. -T.]*

(as opposed to the containment going the other way). Also, just above this, it may be more clear to write let be arbitary as opposed to let be arbitrary, to emphasize that one may take , but must be avoided to assure that the sets we wish to apply Lemma 3.18 to are nonempty.

*[Corrected, thanks – T.]*