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!

This is a section 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.

For full clarity sake, Volume 1 through 7 in English is Yu-Gi-Oh!, 8 through 31 are this series, and 32 through 38 is Yu-Gi-Oh! Millennium World. The Omnibus made by VizMedia covers all 38 across 13 Omnibus Volumes.