typos:
Page 2 line 2: 'we denote it by' should be 'we denote by'
Page 5 line -6: comma after definitions.
Page 8 line 11: the argument works over the real numbers, but not so obviously over the complex numbers. It would be better to say that there is no common eigenspace for the elements of order 3 and order 2.
Page 9 line 12: direct sum symbol missing.
Page 13 line 3: 'representations' should be 'representation'.
Page 19 line 16: Remove the comma after 5.3.3.
Page 24 line -8: 'decomposition' should be 'decomposing'.
Page 26 line -5: Replace 'simple characters' by 'simple representations'. At the end of the paragraph insert an extra sentence: 'As a matter of terminology, if a representation $\rho$ has character $\chi$, we define the kernel of $\chi$ to be the kernel of $\rho$.'
Page 28 line 9: bad line break at the end of the line.
Page 28 line 23: bad line break at the end of the line.
Page 29 line 7.: The sentence runs on and should be replaced by two sentences.
Page 42 line 15: The first sentence of Theorem 3.5.1 should be: 'Let $S$ be a commutative ring with a $1$ and let $R$ be a subring (containing $1$).'
Page 42 line -3: + sign missing before $Rx_n$
Page 66 line -4: V should be W (three times).
Page 66 lines -2 and -3: W should be V (three times).
Page 100 line 16: then should be than.
Page 107 line 15: the left side of the equation should be
\sum_{r\ge 0} \dim ((IG)^r/ (IG)^{r+1})t^r
Page 124 line 4 (in the proof of 7.3.2(2)): With the hypotheses of 7.3.2 it is not true that $U/\Rad U$ is semisimple (this is true in restricted circumstances, such as for modules over a finite dimensional algebra). From line 3 onwards, replace 'The bottom arrow is an essential epimorphism' to the end of the paragraph by
'The bottom arrow $\phi:U / \Rad U \to V/\Rad V$ is an essential epimorphism if and only if it is an isomorphism. We prove that the first statement implies the second. Suppose $\phi$ is an essential epimorphism and let $M$ be a maximal submodule of $U / \Rad U$. Then $\phi(M)\ne V/\Rad V$, and so the induced map $(U / \Rad U)/M \to ( V/\Rad V)/\phi(M)$ is nonzero. Its domain is a simple module, so the induced map is one to one. It follows that the kernel of $\phi$ is contained in $M$. Thus $\ker\phi$ is contained in every maximal submodule of $U/\Rad U$, and hence in their intersection, so it is zero. Because $\phi$ is both one to one and onto, it is an isomorphism.'
Page 126 line 6: Replace the sentence by:
'We define idempotents $e_i\in A/I^i$ inductively, starting with $e_1=e$. For $i\ge 2$ the element $e_i+ I^{i-1}/I^i \in (A/I^i)/(I^{i-1}/I^i)$ will correspond to $e_{i-1}\in A/I^{i-1}$ under the isomorphism given by the third isomorphism theorem.'
Page 128 line 2: The final = before the symbol S should be an isomorphism sign. This isomorphism could also be explained.
Page 136 line 1: '6.12' should be 'Corollary 6.3.7'
Page 136 line 2: '7.14' should be 'Theorem 7.3.9'; '7.13 and 6.3' should be 'Theorem 7.3.9 and Proposition 6.2.1'
Page 136 line 9: '4.12' should be '4.3.7 and Corollary 4.3.8'
Page 137 line 7: '4.13' should be '4.3.8'
Page 138 line -10: '6.4' should be '6.2.2'
Page 138 line -6: '7.14' should be 'Theorem 7.3.9'
Page 139 line -7: '6.2' should be '6.1.2'
Page 139 line -6: Delete '\cdot kH' from the right of the equation. (The deleted symbols are correct, but unnecessary and confusing.)
Page 140 line -10: Delete 'in 4.9 and'
Page 143 line 7: '4.13' should be 'Corollary 4.3.8'
Page 143 line -4: '6.2' should be 'Theorem 6.1.2'
Page 144 line -13: '11.8' should be '11.2.1'
Page 182 line18: 'degree is divisible' should be 'degree divisible'
Page 184 line 18: 'Theorem 9.5.4' should be 'By Theorem 9.5.4'
Page 209 line -1 and page 210 line 3: Probably Ua and Ub should be U_a and U_b everywhere (4 occurences of each). This would look better in the diagrams on page 210, but at least the notation is consistent as currently written.
Page 210 line 6: D_{20} should be D_{30}
Page 211 line 8: 'module' should be 'modulo'.
Page 227 line 15: the final 'RG-module' should be 'RH-module'.
Page 233 line -1: the term $v_{mn-1}$ should be $v_{mn}$ to the right of the = sign.
Page 234 line 2: the matrix should be transposed.
Page 255 line 10: the term $u_{mn-1}$ should be $u_{mn}$ to the right of the = sign.
Page 271 line 4: there may be a space between $U$ and the comma.
Page 308 line 19: 'orthogonal' should be 'orthogonality'.
Page 312 lines 4 and -7: on both lines 'Lemma 5.5' should be 'Proposition 5.2.3 or Example 5.2.4'.
Page 12 Question 4: A possible addition is to prove the if $\phi$ is 1-1 on the socle then $\phi$ is 1-1.