I am quite sure that this question will be marked as duplicate and I am very well aware of all the other threads on the topic, which however do not provide me with a satisfactory answer.
Essentially what I am asking for is a good reference on tensor products of vector space. By reference I mean a pure math reference, nothing like physics/engineering/handwaving.
My background on relevant topics: I think I have a decent understanding of abstract linear algebra (more or less at the level of Axler - Linear Algebra Done Right or Hoffman & Kunze - Linear Algebra - at least first 9 chapters) but I had little exposure to Abstract Algebra (just a little about groups, very very little about rings and fields and zero exposure to modules).
I spent several hours in the library and on Amazon but I surprisingly found very little math material, probably only Greub - Multilinear Algebra, which is maybe a little too heavy for me (but probably as of now would be my best shot).
Also, I am aware of K. Conrad's expository papers "Tensor products I" and "Tensor products II" and, from what I can understand by having a look at them, they would be perfect for me if they were written just in a vector space setting. However the module setting seems a bit too hard for me: I dont even know what a module is but I think I nonetheless have the right to understand what a tensor product of vector spaces is.