Computational geometry concerns itself with designing andanalyzing algorithms for solving geometric problems. Thefield has reached a high level of sophistication, and verycomplicated algorithms have been designed.However, it isalso useful to develop more practical algorithms, so long asthey are based on rigorous methods. One such method is theuse of randomized algorithms. These algorithms have becomemore and more popular, turning into one of the hottest areasof recent years. Dynamic algorithms are particularlyinteresting because in practice the data of a problem areoften acquired progressively. In this monograph the authorstudies the theoretical complexity and practical efficiencyof randomized dynamic algorithms.