What is an English adjective that means "able to learn new things quickly"?

Fast learner or quick learner

I would say clever, quick-witted or, informally, smart:

clever (adjective)
quick to understand, learn, and devise or apply ideas; intelligent.

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quick-witted (adjective)
showing or characterized by an ability to think or respond quickly or effectively.

here are some words that came to mind - sagacious,

Exhibiting or marked by keen intellectual discernment, especially of human motives and actions; having or proceeding from penetration into practical affairs in general; having keen practical sense; acute in discernment or penetration; discerning and judicious; shrewd: as, a sagacious mind.

there's astute,

Quick at seeing how to gain advantage, especially for oneself; shrewd; critically discerning.

and of course, polymathic

Pertaining to polymathy; acquainted with many branches of learning.

and autodidactic :)

Relating to or having the characteristics of an autodidact; self-taught.

The idiom "quick on the uptake" would apply here.

Defintion: quick to understand or learn something.

Example: Just because I'm not quick on the uptake, it doesn't mean I'm stupid. Mary understands jokes before anyone else because she's so quick on the uptake.