  I discuss three different selected topics in top quark physics. The first
topic concerns the next-to-next-to-leading order calculation of the
hadroproduction of top quark pairs and the role of multiple polylogarithms in
this calculation. I report on an ongoing next-to-next-to-leading order
calculation of heavy quark pair production in hadron collisions where the
loop--by--loop part of the calculation is about to be completed. Calculating
the loop-by-loop part allows one to take a glimpse at the mathematical
structure of the full NNLO calculation. The loop-by-loop contributions bring in
a new class of functions introduced only eight years ago by the Russian
mathematician Goncharov called multiple polylogarithms. The second topic
concerns a next-to-leading order calculation of unpolarized top quark decays
which are analyzed in cascade fashion $t \to b + W^+$ followed by $W^+ \to l^+
+ \nu_l$. Finally, I present some next-to-leading order results on polarized
top quark decays which are analyzed in the top quark rest system.
