CORRECTIONS:

1. p. 55, line 4 of 2nd paragraph: to the near H-M and H-M [not H -M] p. 87, line 4. It also

explains  H-M [not H -M] and near H-M p. 87, line 8.  {\sl complements\/} of H-M and near H-M

[not H -M] p. 89, after (8.6): H-M or near H-M  [not H -M] rep.~is

p. 180, 3rd line of 2nd paragraph:  [not H -M] 

2. p. 92: It said: "The cusp pairing for $r=4$ should extend to the case $r\ge 5$, though we don't yet know how." 

We knew how to do that by the time the paper was complete, though we forgot to delete this line.

It now says: "The cusp pairing for $r=4$  extends to the case $r\ge 5$ (\S\ref{genrShInc})." 

p. 93: End of first paragraph of \S1.4.7: Merel-Mazur should be Mazur-Merel. 

3. p. 106: Last line of Prop. 2.17 needed the conclusion to be referencable. It is  now expression (2.19), and references to it now appear as (2.19) instead of (??). 

4. Bottom of p. 107: $|\ni_k^\inn|= (p^{k+1}+p^k)\phi(p^{k})/2$ should be $|\ni_k^\inn|= (p^{k+1}+p^k)\phi(p^{k+1})/2$

5. p. 129: Title of Section 4 should be: [Moduli] and reduced Modular Towers (change "Modular" to "Moduli"). 

6. p. 140: Reference to [Fr01] changed to [Fr02]: and a more precise quote:

[Fr02, Prop. 2.8]:  M. Fried, Moduli of relatively nilpotent extensions, Institute of Mathematical

Science Analysis 1267, June 2002, Communications in Arithmetic Fundamental Groups, 70--94. 

7. p. 160, line 22: as $(u,v)=(\mp(\bg),\wd(bg))$ should be,  as $(u,v)=(\mp(\bg),\wd(\bg))$.

8. p. 180: 1st line of 2nd paragraph of \S9:  Orbits of $\lrang{\gamma_1,q_2}$ should be [Orbits

of $\lrang{\gamma_1,\gamma_\infty}$], to emphasize we view $q_2$ in $\bar M_4$. 

9. Bottom p. 184: $G_{k+1} [acts] trivially on .... 

10. p. 188: Def. 9.11: ${}^T\hat H$ should be ${}^T \hat G$. 

11. Ex.~9.19: The 3rd sentence should be as follows.  

For this case, $\tr(T_{H'}(m))=4=\tr{T_{H'}(m')}$ and $\tr(T_{H'}(mm'))=8$: 

$m,m' \in C_{18}$ and $mm'\in C_{16}$.