Errata which have been fixed in the 2nd printing are marked with a *. To the best of my knowledge, all errata are fixed in the 2nd edition.
News: The 2nd edition is now available at amazon.com or from the Johns Hopkins University Press. (All royalties go directly to charity  half to the Sage Foundation to support opensource mathematical software development, and half to the Earth Island Institute, an environmental organization with projects all over the world.)
Thanks to those readers who emailed or snailmailed me some of the following errata. In particular, I'd like to thank Jamie Adams, Lewis Nowitz, David Youd, Roger Johnson, Jaap Scherphuis, Michael Hoy, Tom Davis, John Rood, Trevor Irwin, Stephen Lepp, Mark Edwards, Carl Patterson, Peter Neumann (seven pages!), Bill Zeno, Herbert Kociemba, Alastair Farrugia, Matthew Lewis, and Christopher Tuffley.
General comments:
[1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0] [1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0] [0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0] [1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1] [1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0] [0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0] [0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0] [0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0] [0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0] [0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0] [0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0] [0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1] [1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1] [0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0] [0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1] [0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1]
My apologies to David Singmaster.
They can be solved by using x_{15}=
0  0  0  1  1 
1  0  1  0  1 
1  0  1  1  0 
0  0  1  0  0 
1  1  0  0  0 
0  0  1  0  1 
1  1  0  1  1 
0  0  1  0  1 
1  0  1  1  0 
1  0  1  0  0 
0  0  0  0  1 
0  1  1  1  0 
1  0  1  0  0 
1  1  0  0  0 
1  0  0  0  0 
0  0  1  0  0 
1  0  1  0  1 
1  0  0  0  1 
0  1  1  1  0 
0  0  1  0  0 



ix, 8  the previous  a previous 
xiii, 8  solved  was motivated by 
6, 6  not a subset of a finite set  not finite 
6, 1  it's  its 
14, 11  fg  fog = fg 
14, 6  S = T.  S = T < infinity.. 
15, 8  f:S > Z  f:Z>S 
16, 9,8  linear transformations  matrices 
19, 11  k = m  k = m+1 
19, 11  a_{ij}  (AB)_{ij} 
19, 9  row of  column of 
20, 1  det(A_{ij})  det(A_{ij})a_{ij} 
21, 2  or  and 
22, 3  21  23 
22, 18  (s,t) belongs to S  (s,t) belongs to R 
*26, 19  Exactly one  Each one 
*26, 20  30  10^{3}=1000 
*26, 9  and  an 
*26, 3  an  and 
27, 12  object  objects 
27, 12  n, n1, ..., nm  n, n1, ..., nm+1 
27, 10  poker hands  "ordered poker hands" 
27, 8  52*51*50*49*48*47 = 14658134400 = (1.4...)x10^{10}  52*51*50*49*48 = 311875200 = (3.1...)x10^{8} 
28, 5  an combination  a combination 
28, 1314  right ... left  left ... right 
31, 15  S^{s}  S^{c} 
33, 13  a point of points  a collection of points 
33, 6  It's  Its 
37, 10  chapter 8  chapter 9 (see Theorem 9.3.1) 
37, 15  then  are distinct then 
38, 15  S_{i}  A_{i} 
43, 18  (n,a_{n})  (n,a_{n1}) 
42, 910  row  column 
43, 14  (b_{n},n)  (b_{n1},n) 
*45, 23  a(ab)^{2}  (ab)^{2}a 
*45, 26  a(ab)^{2}  (ab)^{2}a 
*46, 5  ka(ab)^{2}  k(ab)^{2}a 
*46, 7  k^{2}a(ab)^{2}  k^{2}(ab)^{2}a 
47, 1  five  four 
50, 10  radians  (degrees) 
51, 2  closed geodesic path  closed path 
*52, 9  f_{1}  f_{1}r_{1} 
*61, 18  120 degrees  72 degrees 
67, 1  {i,j,k}.  {i,j,k}, and x doesn't equal y. 
68, 9  D_{2n}  D_{n} 
70, 5  o : G x G x G  G x G > G 
72, 9  What didn't  Why didn't 
76, 16  such that  and a place token p_{i+1} such that 
*76, 3  {1,3,6}  {1,3,4} 
*76, 2  {3,6}  {3,4} 
77, 2  (Lagrange)  ("Lagrange's Theorem") 
78, 7  x in G.  x in G. (Exercise: verify this.) 
78, 8  "so"  "(see Ponderable 2.3.3), so" 
*78, 9  "...belongs to G"  "...belongs to Z(G)" 
79, 13  identifies  identified 
79, 4  likelyhood  likelihood 
*80, 4  M_{D}^{2}  M_{F}^{2} 
*80, 6  ...showed to there ...  ...showed that there ... 
*82, top diagram  label "8" (resp., "6") on cube  label "6" (resp., "8") on cube 
84, 14  ... substitutions  ... des substitutions 
84, 3  g^{h}=1  g^{h}=g 
86, 5  g in G_*  d \geq 0 
*87, 2  clases  classes 
*87, 1011  g*x*g^{1}  g*y*g^{1} 
88, 10  left action  right action 
88, 5  right  left 
88, 3  on the right  on the left 
89, 5  right action  left action 
89, 15  send  sent 
89, 18  are  induce 
89, 19  (though not all are)!  . 
89, 21  In other words,  Roughly speaking, 
89, 2122  group acting on a set at `random'  `random` finite group acting primitively on a finite set 
89, 24  corners  corner 
89, 1, 2  (a), (b)  (b), (c) 
91, 18  set of consisting  set consisting 
*92, 6  right face  down face 
93, 17  sbgroup  subgroup 
93, lines 24,25  groups  subgroups 
94, 15  both and  both an 
95, 89  Then ... G = H* ... maximal). Thus p either ...  Then G = H* ... maximal). This implies p either ... 
95, 10  In either case, the result ... hypothesis.  The result ... hypothesis. 
95, 13  (Lagrange)  ("Lagrange's Theorem") 
*96, 13  a(ab)^{2}  (ab)^{2}a 
99, 8  organisational  organizational 
99, 13  choosen  chosen 
99, 11  always be ... is),  be ... is) is 1, 
*99, 7  .5  1 
99, 7  always  be 
99, 6  always be solved.  be solved is 1. 
100, 18  and shall  and 
*101, 14  (M1)(N1)  N(M1)+M(N1) 
*101, section 6.3.1  Merlin's magic  3x3 light's out 
104, 5  for some  provided 
*104, 7  E_{i,j} in M_{N}  E_{i,j} in M_{MxN} 
*105, 8  omit "Merlin's magic and"  
105, 3  2  3 
105, 4  3  4 
105, 5  4  5 
106, 7  = 0  \not= 0 
107, 20  effectivly  effectively 
107, 14  intorduce  introduce 
107, 9  \cdot F  \cdot : F 
107, 4,3  the vector \vec{0}=(0,0,...,0)\in V satisfies  there is a vector \vec{0}\in V satisfying 
109, 15  if multiplicity  of multiplicity 
109, 16  matrix  square diagonalizable matrix 
110, 17  is uppertriangular. The number of nonzero entries on the diagonal  is reduced. The number of nonzero rows 
111, 2  reculangular  rectangular 
111, 1  Aien  Alien 
*112, figure 6.5.5  The outer pentagon (numbers 711) should be rotated clockwise 36 degrees with respect to the rest.  
*114, 10  matrix T  see above 
*114, 5  15  16 
*114, 3  is 1  is 0 
*114, 2  are initial  are no initial 
116, 11  eminating  emanating 
117, 8  who  whom 
117, 9  laywer  lawyer 
117, 6  v's  v 
*117, 2  (1 2) , (2 3)  (1,2) , (2,3) 
119, 21  Micheal  Michael 
120, 12  who  whom 
122, 6  We can ... path p,  Let a path p on puz(Gamma) to be a sequence of moves 
122, 7  n <= 1  n >= 1 
122, 14  of paths based  of closed paths based 
*122, 12  1415 puzzle  15 puzzle 
123, 1  has  has at most 
125, 9  vertices  edges 
126, line 7,6,5  symmetric  symmetry 
127, 12  (1/2)(...^2 + ..  (1/4)(...^2  .. 
127, 1  transpose identity.  transpose 
128, 9  *B  *A 
128, 10  if an  if and 
129, 34  In particular, ... invertible.  The matrix A is invertible since, by definition, its inverse is ^tA. 
132, 8  permutations of  permutations in 
132, 17  permutations of  permutations in 
132, 17  A_{5} x S_{5}  A_{5} x C_{2} 
138, 1  E. Jordan  C. Jordan 
139, 12  X x X  X x X  Delta (where Delta = {(x,x)  x in X}) 
139, 17  belonging to X  belonging to X, x_{i} <> x_{j} 
139, 17  for each  provided 
139, 15  group  permutation group 
139, 11  [R]  [DiMo], Theorem 7.6A 
141, lines 4,5  , and in ... i,j,k.  , as in section 5.1. 
*141, 20,21  left, right  right, left (resp.) 
*141, 23  Let g  Let x 
141, 8  concept  concepts 
141, lines 7, 6  finite groups  finite simple groups 
142, 9  three cubes  two cubes 
142, 14  for all 1 <= i <= n  provided 1 <= i <= n 
142, 1  for all 1 <= j <= n  provided 1 <= j <= n 
143, 2  <= 1  <= n 
145, 4  E. Galois  Ruffini and Abel 
146, 11  who  whom 
146, 15  normal groups  normal subgroups 
147, 21  isomomorphism  isomorphism 
147, 1  isomorphism between  isomorphism 
150, 14  H acts on X. Note  Note, H acts on X and 
150, 4  is an element  are elements 
150, 3  any element other element of E  each other 
*156, 3  somwhat  somewhat 
*156, 1  H_{1} x H_{2}  H_{1} x_{phi} H_{2} 
157, 19  colun  column 
158, 2,1  (x,y)  g 
158, 1  (x,y)  g 
161, 10  group arose  group, originally arose 
*163, 14  n  n1 
*163, 12  n=2  n=3 
164, 15  Rubik's cube.  Rubik's cube which does not contain a basic move followed by its inverse 
165, 9  , however  . However, 
165, 18  occurance  occurence, 
165, 10  cardiality  cardinality 
166, 10  who  whom 
166, 6  R  The letter scriptR 
166, 5  realtions  relations 
166, 3  relations R  relations scriptR 
*170, 45  should be a horizonal line separating cases 15,16  
172, 13  (a)  . 
172, 11,10  , and in ... {i,j,k}.  , as in section 5.1. 
*178, 1  lu, and bu  lu, bl, and bu 
*180, 3, 4, 7, 8  corner  edge 
*180, 4  vertex  edge 
*180, 5  vertices  edges 
*180, 17  (0,1,0,0,0,1,1,0,0,1,0,0)  (0,1,0,0,0,0,0,0,0,1,0,0) 
180, 1  (S_{V} wr C_{3}^{8})x(S_{E} wr C_{2}^{12})  (C_{3} wrS_{V} )x(C_{2} wr S_{E}) 
181, 12  C_{3}^{8}xS_{V}x C_{3}^{8}xS_{V}  C_{3}^{8}xS_{V}x C_{2}^{12}xS_{E} 
185, 1213  allows us to count its elements easier.  enables us to determine the size of this group. 
186, 1  isomomorphism  isomorphism 
188, 2  of (nontrivial)  of 
189, 9  haiku  poem 
193, 8  x_{1}e_{1} +...x_{n} e_{n}  x_{1}e_{1} +...+x_{n} e_{n} 
194, 15  More generally, let  Let 
194, lines 21, 10  e_{2}^{i2}  e_{2}^{i1} 
195, 6  < F,U > ....  < sigma(F),sigma(U) > isom S_{7}, < rho(F),rho(U) > isom PGL_{2}(F_{5}), 
198, 6  fractions  fractional 
201, 3  enties  entries 
201, lines 12, 14, 16  polyhedra  polyhedron 
205, 7  undeground  underground 
215, 13  S_{E} wr C_{2}  C_{2} wr S_{E} 
216, 2  G  G_1 
216, 2  G  G_1 
217, 1 and 4  G  G_1 
217, 1416  Theorem 13.5.1  see above 
217, 18  possible  possible in G 
217, 9  up  down 
223, 15  isocahedron  icosahedron 
224, 13  in his PhD thesis.  a year after his Docteur es Sciences thesis in 1859. 
225, 18  stating  containing 
225, 11  A_{8}, A_{12}  A_{7}, A_{11} 
229, 8  Matheiu  Mathieu 
230, lines 18,17,7  isocahedron  icosahedron 
230, 14  many experts thought they had classified all finite simple groups  some experts thought all finite simple groups had been classified 
231, lines 7,8,11  parallelpiped  parallelepiped 
231, 20  giving the first proof  giving one of the first proofs 
232, 1  [R], ch. 9  [DM], Theorem 7.6A 
251, 11  Berlekamp  E. Berlekamp 
*253, 17  D. Hofstatler  D. Hofstater 
*253, 17  Metamathematical Themas  Metamagical Themas 
259, 14  E. Jordan  C. Jordan 