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The long-term sustainability of the high-energy physics (HEP) research software ecosystem is essential to the field. With new facilities and upgrades coming online throughout the 2020s, this will only become increasingly important. Meeting the sustainability challenge requires a workforce with a combination of HEP domain knowledge and advanced software skills. The required software skills fall into three broad groups. The first is fundamental and generic software engineering (e.g., Unix, version control, C++, and continuous integration). The second is knowledge of domain-specific HEP packages and practices (e.g., the ROOT data format and analysis framework). The third is more advanced knowledge involving specialized techniques, including parallel programming, machine learning and data science tools, and techniques to maintain software projects at all scales. This paper discusses the collective software training program in HEP led by the HEP Software Foundation (HSF) and the Institute for Research and Innovation in Software in HEP (IRIS-HEP). The program equips participants with an array of software skills that serve as ingredients for the solution of HEP computing challenges. Beyond serving the community by ensuring that members are able to pursue research goals, the program serves individuals by providing intellectual capital and transferable skills important to careers in the realm of software and computing, inside or outside HEP.