Where to continue the Fairy Tail manga

Fairy Tail by Hiro Mashima, 2006. The manga is complete at 545 chapters across 63 volumes.

• Series 1 (175 episodes): Continue the manga from chapter 298 in volume 35.
• Series 2 (102 episodes): Continue the manga from chapter 418 in volume 49.
• Final Series (51 episodes): You are caught up, the anime adapts the manga through chapter 545. The Final Series adapts the Alvarez arc to the manga's ending, so there is nothing left to continue.

Read the manga: Kodansha.