I used Osborne's book for an introductory course on game theory I took as an undergraduate. While Osborne provides a great general overview of game theory, I find this book lacking in a number of respects.
First, theorems are presented in this book inuitively, as opposed to rigorously. Therefore, in place of using proofs to justify a theorem or a given result, many of the theorems are illustrated through words. This method, however, proves to be confusing at many points in the book.
In addition to this, the book is heavily invested in the use of examples to illustrate the numerous applications of particular theorems or results. While I generally applaud the extensive use of examples, this also proves to be very confusing at times since the logical steps Osborne seems to make are not always explicitly stated. This caused me some trouble in trying to solve several problems in the textbook. The one saving grace was that Osborne has posted several (though not all) solutions on his website.
This book does require knowledge of algebra and a little calculus. Some microeconomic theory wouldn't hurt, either--especially for the sections on Stackelburg and Cournot duopolies. Becuase most economics programs in the US stress mathematics, I would recommend an alternative textbook that is more rigorous. Principally, I used Roger Myerson's "Game Theory: Analysis of Conflict" to supplement the shortcomings of this book. Myerson's book is thoroughly rigorous and is, I believe, used as a graduate textbook for game theory in many departments. If, however, you are interested in a general overview of the field or do not feel comfortable with technical mathematics, I would definately recommend this book.