I'm reading Reductive Groups over Local Fields by Tits (from the Corvallis proceedings), and I'm having trouble making sense of several of the definitions, especially when it comes to the local Dynkin diagram. For example, I don't know any examples of groups with non-reduced root systems or with any affine roots $\alpha$ such that $d(\alpha) > 1$ (Here this means that the subgroup $U_\alpha$ corresponding to $\alpha$ has $\dim{(U_\alpha / U_{\alpha + \varepsilon})} > 1$). I think it may be helpful to familiarize myself with a more diverse set of examples of non-split groups to apply these definitions to.
I know Tits has a complete classification of groups by local Dynkin diagrams in section 4, but they are given only by "name" (e.g. $^4D_4$), "affine root system" (e.g. $C\text-BC^{I\!I\!I}_1$), and "index" (e.g. $^2D^{(2)}_{4,1}$), whereas I would hope to find some constructive information about the groups themselves—for instance, involving restriction of scalars or units groups of algebras.
My previous main examples of non-split groups, $SU_n$ and restriction of scalars of a split group over a quadratic extension, do not seem powerful enough to make sense of these definitions. In particular, anisotropic groups have no roots and are trivial as a source of examples. Does anyone know a good source for constructive examples of a diverse range of non-split algebraic groups?
