Radar is one of the most important inventions of the twentieth century.However, until recently, radar has been used mainly for the purpose of detection rather than identification.In the frustrated words of one expert in the search for unexploded ordinance, "we detect everything, we identify nothing". The first effort to address the problem of target identification was the invention and use of synthetic aperture radar(SAR).However, although achieving remarkable success in certain applications,SAR is inherently limited since it is based on the so called weak scattering approximation which ignores both multiple scattering and polarization effects.In recent years, in an effort to overcome the limitations of such an incorrect model, considerable effort has been put into the development of nonlinear optimization techniques which are based on the correct use of Maxwell's equations. Such an approach has achieved some success.However, the success of such an approach is based on strong a priori knowledge of the scattering object and hence is inappropriate for many, if not most, practical applications.In view of the problems inherent in the weak scattering and nonlinear optimization approaches to target identification , a new method has been developed in the past few years called the linear sampling method, which is part of a collection of methods loosely called qualitative methods in inverse scattering theory. This lecture is an introduction for the non-expert on the main mathematical ideas which form the basis of the linear sampling method for electromagnetic waves together with numerical examples showing the practicality of this new approach to the problem of target identification.