I probably would never have gotten my PhD without this book, and it is a stupendous classic.  Nowdays, though, my first resort is always Maple or Mathematica, with their manifold capabilities.  I still find it useful for trying to understand what those programs are doing by way of simplification (or, more commonly, not doing).  Eventually Maple and Mathematica will figure out that they need to couple a powerful explanatory capability to their marvelous algorithms, and this book will become truly obsolete - but that date is not yet here as of 2004.<br>Four stars only because it has been partly overcome by history. 5 Plus for its historical importance.