What is the relationship between Apollo and the Furies? How do they view each other?

The Oresteia is one of many Greek literary works that takes places immediately after the Trojan War. Both the plot of the story and the characters within it would have been familiar to its audience.

The most important information you need to understand the relationship of Apollo to the Erinyes or Furies is actually the background found in Hesiod's Theogony about the generations of the Greek gods. 

According to Hesiod and other ancient sources, the...

The Oresteia is one of many Greek literary works that takes places immediately after the Trojan War. Both the plot of the story and the characters within it would have been familiar to its audience.

The most important information you need to understand the relationship of Apollo to the Erinyes or Furies is actually the background found in Hesiod's Theogony about the generations of the Greek gods. 

According to Hesiod and other ancient sources, the first generation of gods were primordial deities representing such natural elements as Chaos (or the Void), earth, night, and sky. The second generation sprang from these and overthrew them; this second generation was that of the Titans. The Furies were part of this generation. The third generation of Olympian gods (including Apollo) overthrew the Titans, imprisoning many of them or condemning them to eternal punishment.

The Furies are female goddesses of justice who see Apollo's support for Orestes as part of a pattern of the disrespect of the upstart younger gods for an older generation. They also argue that Apollo as a male god is advocating the rights of men in preference to those of women and mothers. Apollo sees the Furies as primordial, irrational, and vengeful. Thus the relationship is antagonistic until Athena, a female goddess of wisdom, creates a brilliant compromise, founding the Court of the Areopagus.