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This article contains the last part of the mini-course `Spaces: a perspectiveview' delivered at the IFWGP2012. Here I deal with the part of the mini-coursewhich centers on the classification questions associated to the simple real Liegroups. I review the original introduction of the Magic Square `a laFreudenthal', putting the emphasis in the role played in this construction bythe four normed division algebras ${\mathbb R}, {\mathbb C}, {\mathbb H},{\mathbb O}$. I then explore the possibility of understanding some simple realLie algebras as `special unitary' over some algebras ${\mathbb K}$ or tensorproducts ${\mathbb K}_1\otimes {\mathbb K}_2$, and I argue that the propersetting for this construction is not to confine only to normed divisionalgebras, but to allow the split versions of complex, quaternions and octonionsas well. This way we get a `Grand Magic Square' and we fill in the detailsrequired to cover all real forms of simple real Lie algebras within thisscheme. The paper ends with the complete lists of all realizations of simplereal Lie algebras as `special unitary' (or only `unitary' when $n=2$) over sometensor product of two $*$-algebras ${\mathbb K}_1, {\mathbb K}_2$, which in allcases are obtained from ${\mathbb R}, {\mathbb C}, {\mathbb H}, {\mathbb O}$and their split versions as sets, endowing them with a $*$-conjugation whichusually but not always is the natural complex, quaternionic or octonionicconjugation.

A perspective on the Magic Square and the 'special unitary' realizations of simple Lie algebras