This text is a solid introduction to game theory for mathematical economists at the graduate level (but apparently logicians love it, too). In principle, the book could be read by someone without any prior knowledge of game theory, but I would strongly advise such a reader to spend some time on a less "dry" text (such as Kreps's "A Course in Microeconomic Theory") before (or at least while) taking up this one.
The authors (like Myerson's "Game Theory" and unlike both Kreps and Fudenberg and Tirole's "Game Theory") cover both non-cooperative and cooperative game theory, with a nice balance.
Two topics not covered in other major texts are "Complexity Considerations In Repeated Games" (Chapter 9) and "Implementation Theory" (Chapter 10). The implementation theory chapter is a wonderful introduction to the topic, but is unfortunately limited to the perfect information case (mechanism design under imperfect information is covered by both Fudenberg-Tirole and Myerson.)
The only application of game theory to which the authors devote considerable space is bargaining (those who know the authors won't be surprised!) - and its treatment could have been a little less abstract.
In sum, it is a very good book that is not dominated by (nor dominates) any of its competitors cited above. If I were to teach a graduate game theory course, I would probably adopt it as the major text and supplement it with papers and parts of the other books.