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This volume contains a representative discussion of mathematical problems that arise in radar and sonar. The design of waveforms for radar and sonar and the development of algorithms for the processing of these waveforms lead to many interesting and difficult problems of applied mathematics. It is timely to separate these prob- lems from the engineering tasks of radar and sonar to form a minitopic of applied mathematics. The range of such problems - applications of group theory, modern topics of signal processing, inverse problems, array processing and beamforming, estimation-theoretic imaging, and phase tracking - cannot be found in any other single volume.