Older version of Illustrator

Adobe only gives access to the two most recent versions of Illustrator as part of a subscription to Creative Cloud. The latest versions do not appear to be compatible with Catalina, however. Catalina also requires 64 bit applications so you would not even be able to install a perpetually licensed version of pre-Creative Cloud (which are all 32 bit programs) from discs with a serial number. You could possibly try contacting Adobe directly and plead your case to them for an older version that could be installed on Catalina (providing that the activation servers for compatible versions have not been shut down). As you can see the prospects do not appear good. You can access the Adobe Help Center at https://helpx.adobe.com/support.html.