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You can use the Media file uploader web part to allow users to upload content to a specific media library.
Note that the Media gallery web part provides the same functionality as the Media file uploader web part but allows users to view the media library content as well. The use of the Media gallery web part is described in Displaying media library content on the live site.
Note that users can only upload a thumbnail if they are uploading a media library file together with it. The thumbnail is attached to the file it is uploaded with.