This is a continuation of the original Yu-Gi-Oh! series and contains the Duelist Kingdom and Battle City arcs. Originally just called Yu-Gi-Oh!, Viz renamed it to its current name.

This series continues in Yu-Gi-Oh! Millennium World

From Viz:
10th grader Yugi spent most of his time alone playing games--until he solved the Millennium Puzzle, a mysterious Egyptian artifact! Possessed by the puzzle, Yugi becomes Yu-Gi-Oh, the King of Games, and challenges evil-doers to the Shadow Games--weird games with high stakes and high risks! These graphic novels contain new stories not seen in the anime, including the origin of Yugi and his friends!

The adopted son of Pegasus J. Crawford, Yakou Tenma, decides to avenge his senpai's defeat at the hands of Yugi Mutou.

The final Yu-Gi-Oh! story! After hundreds of battles, Yugi has finally gathered all the Egyptian God Cards... the key to unlocking his memories of his past life as an Egyptian pharaoh. When Ryo Bakura gives him the Millennium Eye, Yugi opens the door to the "world of memory," and his mind travels back in time to ancient Egypt, when the magic and monsters were real! Now Yugi and his friends must explore the world of Yugi's forgotten past... and fight an enemy who has been waiting for them for 3,000 years!

10th grader Yugi spent most of his time alone playing games--until he solved the Millennium Puzzle, a mysterious Egyptian artifact! Possessed by the puzzle, Yugi becomes Yu-Gi-Oh, the King of Games, and challenges evil-doers to the Shadow Games--weird games with high stakes and high risks! These graphic novels contain new stories not seen in the anime, including the origin of Yugi and his friends!
(Source: Viz)

A two-part prologue special to the movie Yu☆Gi☆Oh!: The Dark Side of Dimensions set between the end of the Yu☆Gi☆Oh! manga and the beginning of the movie.