I'm working on a project and I will need to look at some theory regarding polynomials in noncommuting variables. I have a 1st ed. copy of Rotman's Advanced Modern Algebra, which I've been getting some of my theory from (There is a pdf version of the 2nd ed. you can find online by googling). On page 724 of the same text is where he offers the definition for the Ring of polynomials over $R$ in noncommuting variables $X$, denoted $R\langle X\rangle$. The definition verbatim is as follows
$\textbf{Definition}$: If $R$ is a commutative ring and $V$ is a free $R$-module with basis $X$, then $T(V)$ is called the ring of polynomials over $R$ in noncommuting variables $X$, and it is denoted by $R\langle X\rangle$.
On page 725 he continues on just a little about the subject but its not much help to my own understanding. So what I was hoping to ask for were some recommendations of resources regarding this topic that might aid in my understanding of the material. I've tried to look for some results myself but I haven't found anything helpful yet; I have a feeling that it might be due to the fact that I'm not familiar enough with the algebra jargon currently in use.