I'm reading a lecture note here : http://www.cis.upenn.edu/~cis610/diffgeom7.pdf
It introduces $T^{•,•}(M)$ the tensor algebra and says that this is a necessary tool in differential geometry. Well, this is the first time I see this variant tensor algebra (I only know the tensor algebra by standard means) and there is almost no detail about this in the link. All there given is almost just the definition. Is there a text introducing this variant tensor algebra formally?
Thank you in advance.
( To be clear, if $M$ is an $R$-modules where $R$ is a commutative ring, $T^{i,j}(M)$ is defined as the tensor product of $i$-times tensor product of $M$ and $j$-times tensor product of $M^*$. And $T^{•,•}(M)$ is defined as the direct sum of those with the natural operation that makes it an algebra)