Which Titaness was the mother of the Muses?

The Titaness who was the mother of the Muses was Mnemosyne.

Mnemosyne was the Titan goddess of memory and remembrance, and Greek tradition made her the mother of the nine Muses by Zeus. Her name comes from the Greek word mnēmē, meaning “memory,” linking her directly to the preservation of knowledge, poetry, music, and cultural tradition.

According to the commonly cited myth, Zeus spent nine consecutive nights with Mnemosyne. Their union produced the nine Muses: Calliope, Clio, Euterpe, Erato, Melpomene, Polyhymnia, Terpsichore, Thalia, and Urania. Each became associated with a field such as epic poetry, history, music, tragedy, comedy, dance, or astronomy.

Mnemosyne was a daughter of Uranus and Gaia, which made her one of the older divine generation and an aunt of Zeus. She should not be confused with the Muses themselves, nor with Lethe, the river of forgetfulness. In some later or alternative genealogies, authors gave her different parentage, but the standard mythological answer remains Mnemosyne.