Who is Zeus's favorite child, the goddess of wisdom and war ? How was she born?

Athena is Zeus' favorite child. Athena had no mother, as she was born full grown in armor from her father's forehead.

Athena was the favorite child. She was indeed born out of Zeus's head, athough that doesn't mean she doesn't have a mother. Her mother was the godess of thought, Metis. Metis drifted into thought while inside Zeus. but it does not mean she isn't her mother still. not long after Metis became athought Athena did to she made her way up to Zeus's head and gave him a massave headache while at dinner and Hephasteus cut his head open and out came Athena fully grown with armor.