Learn Swedish: Kvaliteten på sådant tyg är otrolig. - The quality of such fabric is incredible.

sådant means "such" or "that kind of". It takes the neuter form ending in -t here because it describes tyg (fabric), which is an ett-word (ett tyg). If it were describing an en-word like en tröja (a sweater), you would use sådan tröja.

Why is it just tyg (indefinite) and not tyget (definite)?

After the words sådan, sådant, and sådana, the noun is always in the indefinite form. It works exactly like English: we say "such fabric", not "such the fabric".

Doesn't på mean "on"? Why is it translated as "of" here?

While på most commonly means "on", Swedish uses it to link a property to an object where English would use "of". You will see this specific pattern a lot with things like kvaliteten på (the quality of), priset på (the price of), or namnet på (the name of).

Why is the adjective at the end otrolig (without a -t), when the closest noun tyg is an ett-word?