How Can You Create Your Own Mathematical Space and Explore Embedding Techniques?

[Winzer]

I would like to really get to know the ins and outs of spaces in general.
I would also like knowledge in embedding.

My first goal is to make my own space with certain properties I need/want.
My second goal would be to take some equation and imbed it in my own space.
Unfortunately my math background goes up to PDE's and complex variables.
I will have graduate math physics under my belt in the future.

I am looking for advice in terms of textbooks and possible math courses I could take.
Thanks.

 

[Winzer]

Pretty Please!

 

[HallsofIvy]

I doubt that anyone has any idea what you are asking! There are a variety of different mathematical fields that use the term "space". Are you referring to topology? Are you referring to differential geometry? Or are you talking about "space" in the physics sense?