The counterfeit coins problem is a well-known and important one in combinatorial search theory. The problem may be simply described as that to spend the least number of weighings by a balance to find all the counterfeit coins in a set of coins. With the fascinating and interesting features, and for which there have been found some important applications to the other branches of sciences, it has been an active research topic. In this book there are included the author's main work on this topic, in the chapters 2, 3 and 4 we have presented our results for its three versions, that is the version of the number of fakes is not known beforehand, the version of multi-sets and the version the number of fakes is known in a range respectively. In the end of the book are four appendices including most of algorithms appeared in chapters 2,3 and 4 respectively.