Did Geralt Have Aerondight?

Aerondight is a unique Silver sword introduced in The Witcher. Geralt receives the sword from Lady of the Lake. It symbolizes Geralt's role as The Sword of Destiny. The blade was once owned by a "great warrior" but was left in the depths of Lake Vizima near Black Tern Island where Dagon resided.

Does Geralt have Aerondight in the books?

No, it's a game sword only. It's a clear reference to Excalibur and given the various connections of the saga to the King Arthur story, it's not unusual for CDPR to have added it in. Shame.

How did Geralt get Aerondight?

After Geralt completes the Hermit's tasks and defeats him in a trial of combat, he'll disappear into the lake and reappear as the Lady of the Lake, who will then give Geralt Aerondight.