p. ?at the end of the implication of (ii) from (i) in Proposition 1.2.1, “$\varepsilon k |F|/2$ pairs $v,w$” should be “$\varepsilon k |F|/2$ ordered pairs $(v,w)$“, the right-hand side of $\varepsilon |F|/2$ in the next display should be $\varepsilon k |F|/4$, and the lower bound for $h(G_n)$ should be $\varepsilon k/4$ rather than $\varepsilon/2$.
p. ?In Exercise 1.2.3(i), “two-sided” should be “one-sided”.
p. ?In the proof of Proposition 2.2.8, the Haar measure on $GL_d$ needs to be Lebesgue measure divided by $|v_1 \wedge \dots \wedge v_d|$. The Haar measure of the $w_1,\dots,w_{d-1}$ should then be $O(1)$ rather than $O(1/|v_d|)$, and similarly for the integral in the next display; but to compensate for this, the integral should be against $\frac{dv_d}{|v_d|}$ rather than $dv_d$.
p. ?In Exercise 2.0.4, replace the hint with “you may assume without proof Petersen’s 2-factor theorem, which asserts that every $k$-regular graph with $k$ even can be decomposed into $k/2$ edge-disjoint $2$-regular graphs. Now use the previous example.”.
p. 51Before Exercise 2.3.2, “total mass” should be “total variation”,
p. 74Remark 3.3.7, second line: “(pseudo-)randomly sowing” should be “(pseudo-)randomly sewing”
p. 89Lemma 4.1.3, fourth line: “$a\in A$ and $b\in B$” should be “$a\in A'$ and $b\in B'$”
p. 93Lemma 4.1.7, last line: “$g\in H$” should be “$g\in G$”.
p. 95Proof of Lemma 4.1.7, last line: “$|gH\cap A|\ll K^{-O(1)}|A|$” should be “$|gH\cap A|\gg K^{-O(1)}|A|$”
p. 98Proof of Lemma 4.2.2, eighth line: $\mu^{*n} \|)_\infty$ should be $\|\mu^{*n} \|)_\infty$.
p. 102Exercise 5.0.1, seventh line: add right parenthesis after “should not actually depend on $d$“. Also, “Girth bound” should be “Diameter bound”.
p. 103-104Proof of Theorem 5.0.2, last line of 103 and first two lines of 104: “If $h\in H'$, then $A$ and $Ah$ both lie in $H'$” should read “If $h\in H'$, then $A$ and $Ah$ both lie in $gH'$“, and both occurrences of $AA^{-1}$ should be $A^{-1} A$.
p. 109paragraph 3, first line and third-to-last line: “Lemma 5.1.3” should be “Lemma 5.1.7”
p. 121proof of Lemma 5.3.2:”$A^2$ can be covered by $K$ copies of $A$” should be “$A^2$ can be covered by $K$ translates $aA$ of $A$, and we can restrict to those $a$ in $A^3$ since otherwise $aA$ will not intersect $A$“. Then, later in the proof, $a \in A$ should be $a \in A^3$, $A^7$ should be $A^{10}$, $K^6 |A|$ should be $K^9 |A|$, and $K^{-2C-11}$ should be $K^{-2C-14}$ (three occurrences). In Exercise 5.3.2, add the hypothesis that $V$ is not the one-dimensional space spanned by the identity element.
p. 122Proof of Proposition 5.3.3, third line: “$|A^2\cap B|\leq K^{-C}|B|$” should be “$|A^2\cap B|\leq K^{-C}|A|$“
p. 140Exercise 6.1.3, part (ii): Add the hypothesis that $a$ is not the identity element of $\Gamma$
p. 140last paragraph, second line: The definition of $\mu$ is missing a right parenthesis.
p. 142second paragraph, fifth line: “sufficiently small $\mu$” should be “sufficiently small $c$“.
p. 142In (1.66), $D_+$ should be ${\mathcal D}_+$.
p. ?In (7.10), $1_{n=p_1\dots p_k}$ should be $1_{n=p_1 \dots p_k m; (m,P(p_k))=1}$.
p. 152third line: “in the $\mathcal{D}_{+}$” and “in the $\mathcal{D}_{-}$ case”, should be interchanged.
p. 155Exercise 7.1.4, part (i), displayed equation: “$\pi_2(x,z)$” should be “$\pi_{*}(x,z)$“
p. 155Exercise 7.1.4, part (i): $\sum_{p\leq x,p\equiv 1\pmod{4}} \frac{1}{p}$ is $\frac{1}{2}\log\log{x}+O(1)$, not $\frac{1}{2}\log{x}+O(1)$
p. 155Exercise 7.1.4, part (ii): “infinitely natural numbers” should be “infinitely many natural numbers”
p. 157Theorem 7.2.1, second-to-last line: $K_{\phi(i+1)}/K_{\phi(i)}$ should be $K_{\sigma(i+1)}/K_{\sigma(i)}$
p. 160-161after the proof of Corollary 7.2.3: All appearances of $\Gamma$ and $\Gamma'$ should instead be $\Lambda$ and $\Lambda'$.
p. 162last paragraph, first sentence: “Theorem 7.0.1” should be “Theorem 7.3.1”
p. 164fourth line: “hyopthesis” should be “hypothesis”
p. 208In Exercise 10.1.2, “defined as the closure” should be “defined as the completion”.
p. 213In Exercise 10.2.1(i), “Liouville’s theorem” should be “the maximum principle”, and the phrase “viewed as a function of $x$ and $t$ should be added.
p. ?In the introduction to Chapter 11, ${\mathfrak a}_1 . ({\mathfrak a}_2 . \ldots ({\mathfrak a}_{k-1} . {\mathfrak a}_k) \ldots )$ should be $(\dots ({\mathfrak a}_k . {\mathfrak a}_{k-1}) \dots . {\mathfrak a}_2 ) . {\mathfrak a}_1$.
p. 252In Corollary 11.7.2, the conclusions about certain combinations of $\alpha,\beta$ not being roots is incorrect and should be deleted.
p. 254In Lemma 11.7.8, a fourth case needs to be excluded involving three chains of simple edges of length 1,3,3, which can be treated by essentially the same argument as in (c) (or (b)).
Contributors
Thanks to all those who have contributed corrections. Corrections received on or before 2026-07-09 were reported by the readers listed below over the years; individual per-erratum attributions for these legacy entries were not preserved in migration.