What is universal grammar?

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Universal Grammar is derived from the idea that humans have some sort of cognitive faculty that allows us to process language as well as we do. The idea has to do with the fact that there are certain pieces of grammar that are argued to be shared by all the world's languages. For example, grammatical categories like noun and verb are thought to be common to all the languages of the world. (some grammatical categories like adverbs exhibit more variation). Because the languages of the world share certain properties, the notion is that these shared properties are the byproduct of how we're wired. In addition, each generation is able to learn to use language from the previous generation with relative ease just from exposure. Universal grammar is proposed as a way of explaining why we are able to acquire and use language as well as we do and why, despite the enormous amount of diversity in the languages of the world, we create grammars that are similar to the other grammars that exist. The wikipedia page for universal grammar might also be helpful.

I am not a linguist but would also like to mention the idea of Universal Symbolism, talked about by Carl Jung - he believed (and I agree) that there are universal associations/symbols/metaphors in the world. I would love if someone on this thread might be willing to point me to any existing research that backs up my own personal theory that Universal Language creates Universal Symbols.