While the majority of autonomous driving research has concentrated on everyday driving scenarios, further safety and performance improvements of autonomous vehicles require a focus on extreme driving conditions. In this context, autonomous racing is a new area of research that has been attracting considerable interest recently. Due to the fact that a vehicle is driven by its perception, planning, and control limits during racing, numerous research and development issues arise. This paper provides a comprehensive overview of the autonomous racing system built by team KAIST for the Indy Autonomous Challenge (IAC). Our autonomy stack consists primarily of a multi-modal perception module, a high-speed overtaking planner, a resilient control stack, and a system status manager. We present the details of all components of our autonomy solution, including algorithms, implementation, and unit test results. In addition, this paper outlines the design principles and the results of a systematical analysis. Even though our design principles are derived from the unique application domain of autonomous racing, they can also be applied to a variety of safety-critical, high-cost-of-failure robotics applications. The proposed system was integrated into a full-scale autonomous race car (Dallara AV-21) and field-tested extensively. As a result, team KAIST was one of three teams who qualified and participated in the official IAC race events without any accidents. Our proposed autonomous system successfully completed all missions, including overtaking at speeds of around $220 km/h$ in the IAC@CES2022, the world's first autonomous 1:1 head-to-head race.