[4] The seven chapters of the book are largely self-contained, and consider different problems combining tessellations and algebra.
This result was resolved positively by Hajós's theorem in group theory,[1] but a generalization of this question to non-lattice tilings (Keller's conjecture) was disproved shortly before the publication of the book, in part by using similar group-theoretic methods.
[1] The final chapter returns to the topic of the first, with material on László Rédei's generalization of Hajós's theorem.
[2] Reviewer William J. Walton writes that "The student or mathematician whose area of interest is algebra should enjoy this text".
The award citation called it "a simultaneously erudite and inviting ex- position of this substantial and timeless area of mathematics".