I'm happy to help you with your query about downloading Adobe Illustrator (AI) for free、However, I need to clarify that Adobe Illustrator is a professional graphic design software that is part of the Adobe Creative Cloud suite, and it is not available for free download in its full version.

That being said, there are a few options you can consider:

1、Free Trial: Adobe offers a free trial for Adobe Illustrator and the entire Creative Cloud suite、You can download and use the software for 7 days without paying a dime、After the trial period ends, you'll need to subscribe to a plan to continue using the software.
2、Adobe Creative Cloud Free Plan: While not entirely free, Adobe offers a limited free plan that includes access to some Creative Cloud apps, including a simplified version of Illustrator on the web (Adobe Illustrator on the web)、However, this version has limited features compared to the full desktop application.
3、Alternatives to Adobe Illustrator: If you're looking for a free alternative to Adobe Illustrator, there are several options available, such as:
* Inkscape (free and opensource vector graphics editor)
* Gravit Designer (free vector graphics editor with some limitations)
* Vectr (free vector graphics editor with a simple interface)

Keep in mind that while these alternatives can be great for basic vector graphics editing, they might not offer the same level of features and functionality as Adobe Illustrator.

If you're a student or educator, you might be eligible for a discounted or free Adobe Creative Cloud subscription through Adobe's Education Discount program.

Let me know if you have any further questions or if there's anything else I can help you with!