In this paper, we study the mutual information in a radar system. Radar is a target-detection system that uses echo signals to locate the targets. Echo signals can provide sorts of information about the targets, such as range, azimuth, altitude, velocity, size and so on. In this paper, we employ the thoughts and methodologies of Shannon's information theory to systematically establish an information theory for a radar system in the presence of complex Gaussian noise. Particularly, we focus on targets' location information and amplitude-phase information. First, we derive a theoretical expression of location information in a single target detection assuming the target is uniformly distributed in the observation range. In addition, we approximate the expression in the high signal-to-noise regime and provide a closed form expression of the location information. Second, we obtain an expression to calculate the amplitude-phase information in a single target detection theoretically. Last, supposing that the interference between any targets is negligible, we prove that the detection information in the multiple targets detection is the sum of that in the corresponding single target detections.