Which giant is the father of the goddess Skaði?

The giant who is the father of the goddess Skaði is Þjazi.

Þjazi is a powerful jötunn and one of the most prominent giant figures in the Prose Edda. He is best known for abducting Iðunn, keeper of the gods' youth-preserving apples. After Iðunn's disappearance causes the gods to age, Loki rescues her, and the gods kill Þjazi during his pursuit in eagle form.

Skaði then travels to Asgard wearing her armor and demanding compensation for her father's death. The gods negotiate a settlement: she may choose a husband by looking only at the suitors' feet, leading her to select Njörðr, and she is also promised the ability to make the gods laugh. In another tradition, Þjazi's eyes are placed in the sky as stars.

The sources preserve conflicting claims about who killed Þjazi. Skáldskaparmál credits the gods collectively, while poems attribute the deed variously to Odin, Thor, or Loki. That disagreement does not affect the family relationship: Þjazi is consistently presented as Skaði's father. Suttungr, Hrungnir, and Ymir belong to different giant stories.