  Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely
classified in a series of three papers. This last one classifies the case of
$a^3b$-quadrilaterals with some irrational angle: there are a sequence of
$1$-parameter families of quadrilaterals admitting $2$-layer earth map tilings
together with their basic flip modifications under extra condition, and $5$
sporadic quadrilaterals each admitting a special tiling. A summary of the full
classification is presented in the end.
