Book 2, version 2022-07-27, section 6.8
In some places $f$ is used to indicate the true function and in other places a variable in $p(f | \mathcal{D}_n)$. Some of the suggestions below are to try to reduce potential confusion.
page 273, Algorithm 5: line 1: Following [Fra18], you may wish to substitute: from random queries $\mathbf{x}_i$ -> from an initial space-filling experimental design line 7: What do you mean by $p(y_{n+1} | \mathbf{x}_{x+1}, f)$? I'd recommend simply saying: Update model $p(f | \mathcal{D}_{n+1})$
page 275, line 30: $\mathbb{E}[f(\mathbf{x}_i)]$: Do you mean $\mathbb{E}_{p(f | \mathcal{D}_n)}[f(\mathbf{x}_i)]$? If so, it may be better to be explicit to avoid confusion. page 275, line 33: expeced -> expected
page 276, formula 6.225: $\tau$ -> $V_n$, $\gamma(\mathbf{x})$ -> $\gamma(\mathbf{x}, V_n)$
page 277, line 3: introduced -> introduce