Automated target tracking is a necessary function of the airborne radar and radio control systems. At the present time, there is no a classified approach to design and construct the principles, functioning features, methods, algorithms and procedures of synthesis and analysis of the airborne radar target tracking systems by the range, velocity and azimuth satisfying all long-term requirements. The present Volume 1 “Air-borne Radar Systems and Single Target Tracking” of the two-volumes book “Target Tracking by Airborne Radar Systems” is intended to cover demands of this uncertainty. Contains factual information about the current status of the automated airborne radar target tracking systems that is useful to a wide range of expert participants in and out of the uniform, radio engineers, radar engineers and designers, and others. Deals with the several new perspective methods of the synthesis and analysis and designing the air-borne radar target tracking systems Discusses new theoretical approaches to design the airborne radar target tracking systems are in this Volume. Deals with the general theoretical problems of synthesis and analysis of the information-controlled systems based on the modified statistical theory of optimal control and estimation, not only the classical theory. Presents general information about the integrated on-board and control systems and possible ways to improve the airborne radar target tracking system performance. Additionally, there are a lot of application examples confirming the theoretical results. Under discussion of the specific algorithms of the airborne radar target tracking system operation, a great attention is paid to the methods of synthesis and analysis of the suggested algorithms. The procedure of algorithmic realizations is delivered in detail that will be useful without any doubts for the radio and radar engineers, radar experts, MS and PhD students. A great attention is paid to the design problems of new airborne radar system generation and analysis of operation principles and modes.