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Datasets for autonomous cars are essential for the development and benchmarking of perception systems. However, most existing datasets are captured with camera and LiDAR sensors in good weather conditions. In this paper, we present the RAdar Dataset In Adverse weaThEr (RADIATE), aiming to facilitate research on object detection, tracking and scene understanding using radar sensing for safe autonomous driving. RADIATE includes 3 hours of annotated radar images with more than 200K labelled road actors in total, on average about 4.6 instances per radar image. It covers 8 different categories of actors in a variety of weather conditions (e.g., sun, night, rain, fog and snow) and driving scenarios (e.g., parked, urban, motorway and suburban), representing different levels of challenge. To the best of our knowledge, this is the first public radar dataset which provides high-resolution radar images on public roads with a large amount of road actors labelled. The data collected in adverse weather, e.g., fog and snowfall, is unique. Some baseline results of radar based object detection and recognition are given to show that the use of radar data is promising for automotive applications in bad weather, where vision and LiDAR can fail. RADIATE also has stereo images, 32-channel LiDAR and GPS data, directed at other applications such as sensor fusion, localisation and mapping. The public dataset can be accessed at http://pro.hw.ac.uk/radiate/.