The Leviathan (until an actual name is decided/announced, I'm going to go ahead and take the small assumption that "Leviathan" in actually the ship's name, because all ships need a name) would of been constructed by one of the Imperial powers during The Great War. From context clues and in-game hints, (and Muse just saying it) we know that the Guns of Icarus universe exists in an alternate history of Earth, post WWI, where there was no Interwar Period. The Great War would of truly been the last great war, as the Earth declines technologically and ecologically do to various reasons (I'm going to go out on a limb and say pollution would of been one of them). This would put The Leviathan right on the tail end of the WWI Naval Arms Race between the emerging European Imperial/Industrial powers at the time; Great Britain, France, Germany, and Russia. Historically this arms race reached its peak with the creation and mass-production of the Dreadnought-class war ships. But, there is no reason to think that had WWI not come to an end, an advancement in military thinking would of never taken place. "Bigger is Better" would of still been the main military mind set. Bigger guns, tanks, ships, zeppelins all would of been top priority for military designers at the time. And the GoI landscape confirms that. Aside from The Leviathan, several large battleships and dreadnoughts litter the ground on most of the maps. Several of these maps, Northern Fjords, Anglean Raiders, and Fight over Firnfield all have massive artillery pieces on them, or in the sky-scape just on the horizon. The important thing to note about all of these, and The Leviathan is that they all appear to have rusted at about the same rate of time, long enough where no base metal is exposed, but not long enough where they would collapse in on themselves.
As for what The Leviathan would have actually looked like, my best guess is that it would of been some form of larger, alternated superstructure of a Dreadnought. In constant war coming up with new designs is a hard thing to do, and many times small (or in this case large) changes in size or other variables are all that is made to try and improve upon something (for a good example of this in action, just look at the USAF F-82 fighter from WWII). Hopefully sometime in the near future with the release of Co-op Mode, Muse will publish a more fleshed out lore/history for their game and this "Leviathan Mystery" can be put to rest.
