This article explains what an ABW file is and how to open, edit, and convert it on your computer.
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Both AbiWord (for Windows) and LibreOffice Writer (Windows, Linux, macOS) can open ABW files.
Because ABW files are saved using XML, you can also open them with a text editor, which is great if you don't want to bother installing one of the programs mentioned above. This doesn't format the document properly, however, so you'll see a lot of things that you wouldn't if you opened it in a word processor. Still, it's a great way to see what's in the document and copy text if you need to.
If you are already using AbiWord or LibreOffice Writer, you can open the file in one of those programs and then save it in a new format. For example, AbiWord can convert to Word formats such as DOCX and DOC, and also to RTF, TXT, EML, ODT, SXW, etc.