On the Rain-Slick Precipice of Darkness/Episode One

Although the cases are numbered, they're not completed in that order and in fact several overlap, with items gained and locations unlocked partway through some cases that are required for completing cases opened much earlier in the game.

The majority of the game's plot takes place in Case 2: The Game Is Afoot, with other cases being completed to gather items required for the main story.

Prologue
"Four Gods wait on the windowsill, Where once eight Gods did war and will,

And if the Gods themselves may die, What does that say for you and I?"

- The Quartet for the Dusk of Man