Group testing has been used in medical, chemical and electrical testing, coding, drug screening, pollution control, multiaccess channel management, and more recently in data verification, clone library screening and AIDS testing. The mathematical model can be either combinatorial or probabilistic. This work is a summary of all important results under the combinatorial model, and it demonstrates their applications in real problems. Some other search problems, including the famous counterfeit-coins problem, are also studied in depth. This second edition is updated and embraces the growing importance of two topics: nonadaptive algorithms and error tolerance. Two new chapters, one on clone library screening and the other on error tolerance, have been added. Also included is a new chapter on counterfeit coins, and the chapters have been reorganized into parts to provide focuses and perspectives.