Do I need to play The Withcer 1 & 2 before playing 3?

You don't need to play 1 and 2 prior. Here's a recap:

The games are new non-canon stories by the game studio and are inspired by the Witcher books that were written way back. The books end with Ciri off somewhere in a parallel world after transporting her adoptive parents Geralt and Yennefer to the afterlife so the two can finally exist ever after in peace. This is where the Witcher 1 game begins.

In Witcher 1, the Wild Hunt wants Ciri for her blood/power so they kidnap Yennefer as bait to draw out Ciri. Geralt chases after them and with the help of Letho and his crew they fight the Wild Hunt to a stalemate so Geralt offers his soul in exchange for them freeing Yennefer. To repay a debt to Geralt, Letho looks after Yennefer (whose memory was wiped by the Hunt when they let her go) until they are both captured by Nilfgaard, aka the Empire, the "Black Ones" ruled by Emhyr. Emhyr's mages restore her memory and learn of the lodge by probing her mind. Geralt rides with the Hunt for a bit until Ciri comes and yanks him free, but the Hunt manages to wipe his memory too before she manages to deposit him near Kaer Morhen. This is where the game starts.

In Witcher 2, Emhyr makes a deal with Letho to go and sow chaos in the Northern Realms by assassinating kings and blaming it on the lodge of sorceresses, in exchange for restoring his Viper witcher school. Emhyr wants to soften the north as a prelude to his invasion. Geralt, who's trying to piece his memory back together, gets caught up in this whole kings/dragons/conspiracy stuff.

Witcher 2 ends 6 months before the start of Witcher3. At the beginning of those 6 months, Geralt finally got all of his memory back and took off with Vesemir to find Yennefer. During those 6 months, Ciri has been spotted appearing around the world. Emhyr learns of this and offers Yennefer a deal: save Ciri in exchange for your freedom(Yen was in a Nilfgaard jail during W1 and W2). She tries but discovers using magic to track Ciri only draws the Hunt closer, so she sends a letter to Geralt for his help using more traditional means. This is where Witcher 3 starts

If you are interested in the lore check out the books: https://www.reddit.com/r/witcher/comments/3qm8p9/so_you_want_to_read_the_witcher_books_guide/

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