How do I export Adobe Illustrator (AI) layers from QGIS?
I have tried all the "save as" files from layer and non of them worked.
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As @Mapperz suggested, you can save a layer as a DXF from QGIS. The DXF can be imported into Illustrator easily enough, though you may have issues with scaling.
However, as Illustrator drawings are often set up as standard pages, it's probably better to create a print composer and save the page as either an SVG or a PDF.