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AZW is the book format used by Amazon for their market leading Kindle e-reader.
The format is proprietary and Amazon adds DRM to protect the books it sells via the Kindle store.
Amazon offers a Digital Text Platform site for those who want to publish for Kindle, or convert to AZW.
While Amazon only sells AZW, the Kindle supports TXT, PDF, Audible (Audible Enhanced (AA, AAX)), MP3, unprotected MOBI.