Have similar theories like knot theory been developed in higher dimensions? Well, my question is kind of basic but I hope it would be taken seriously by the community. Also, I'm very new to this topic and I want to study knot theory in future. Knot theory is the study of embedding $S^{1}$ in $\mathbb{R}^3$. Right?
So, it seems reasonable to consider embedding $S^n$ in $\mathbb{R}^m$ for appropriate $(n,m) \in \mathbb{N}\times\mathbb{N}$. Are there any well-developed theories for these embeddings? If yes, is there a name for these theories? Are there any references to learn about them?
Also, I would be happy to know about some self-contained and good references to learn about knot theory and these higher order theories.

A reference to higher-dimensional knot theory: 
E. Ogasa, Introduction to higher-dimensional knots. 
For classical knot theory, I like the book
D. Rolfsen, "Knots and Links". 
It is a bit dated (written by 1970s) but very readable. 
