With the conclusion of Demon Slayer: Kimetsu no Yaiba – Entertainment District Arc, you might be looking to continue the manga right after the anime. A Swordsmith Village Arc begins in volume 12 of the manga. The cover of the volume is below: 586j4y
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VIZ publishes the manga in English, and they describe the story of this volume:
For the first time in over 100 years, the upper ranks of Muzan Kibutsuji’s Twelve Kizuki are not full. Angered, Muzan dispatches the survivors on another mission. Elsewhere, Tanjiro journeys to a village of swordsmiths and has to explain how his sword was so badly damaged to Haganezuka, the smith who made it. While Tanjiro waits for his sword to be repaired, enemies close in…
If you want to continue the Demon Slayer manga right after the Entertainment District Arc anime, you should start with chapter 98, which is the first chapter in volume 12. You can also read every chapter for free this year!
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©Koyoharu Gotoge / SHUEISHA / Aniplex / ufotable