The Campaign Map
The campaign map represents an arean of the gigantic world of Icario. It consists of a large hex grid of provinces of varying size connected by traversible pathways. This guide will cover using the map and what you should try to conquer.
Provinces and footprints
The map is made of provinces (territories). Each has a footprint of one to three hexes. Larger provinces are more valuable: a province's resource output, industry and defensive strength are all a linear function of its size, so a big three-cell province is worth roughly three times a lone single-cell one. However, it is defended much more heavily as well, and you probably won't be able to conquer these with your starting army.
Traversal
Provinces are joined by connections rather than simple adjacency. Two provinces sitting side by side are only neighbors if a link is drawn between them. Armies and sightlines travel only along these links.
Every capitol gets at least four connections of its own, and capitols are guaranteed to all have paths to each other. Different province types may cost more or less to move through, so movement across your territory is not always straightforward. You also may not traverse through enemy provinces; your army will stop and fight there if you try.
Terrain and affinity
Every province has a terrain type, elevation, and resource affinity. Resource affinity dictates how rich its ground is in metal or ichor. Affinity is where your raw income comes from: the more a province leans toward a resource, the more of it you collect each turn from holding it (see Economy & Production). Some provinces also carry an inherent industry bonus, boosting how fast it can build and produce units, or a science boost. Finally, the terrain type can heavily influence any battles that occur on that territory.
Province features can also decide what you can build there. A metal-rich area is needed for a mine, an ichor seam for an ichor mine, or high elevation for some faction structures. Terrain also shapes the battlefield if a fight breaks out on that hex. The battlefield meaning of terrain and elevation is covered in Terrain & Environment.
Most provinces are ordinary ground: plains, woodland, rocky highlands, snowfields, dust flats and mire. A few, however, are important landmarks worth spending some extra effort to conquer. Ferrocrete ruins are thick with salvage and hold archives to study studying, giving them strong metal and science income. Revetment lines earn very little, but hold the entrenchments, fortifications, and logistics structures of past battles, so they're-applied easier to develop and hold larger garrisons than their income suggests. A resonance bloom provides the richest ichor income on, but offers little else due to lack of solid ground to build on. Mire is also heavy with ichor, but just as hard to build on due to the wet, swampy terrain. However, for a faction with unit designs that can navigate that terrain well, it can become a serious defensive advantage. Thermal vents pay well in both resources and caustic pans pay in ichor, but both punish anything that lingers on them in a fight unless resistant to their effects.
Each of these terrains is represented on the battlefield during fights in that territory. A battle over a ruined province is fought through its streets, and one over a ruin standing on high ground forces the attacker to climb to reach the defenders, offering an advantage to the defending line. A single battle in a mire can make hovering and water-resistant Icaroids earn their keep, while resonance blooms can empower the weapons of units standing near them.
Capitols
Your capitol is your home province and the heart of the whole game. You must hold all capitols to win, and losing it shuts your economy down (see the overview). Capitols are always difficult to conquer: each has a full three-hex footprint, and each is guaranteed at least two small single-hex provinces right on its doorstep as easy first conquests to expand into.
Gem deposits
Some provinces hold a gem deposit, drawn as a tinted diamond on the map. Deposits are rare and valuable: holding one grants a slow income of that gem type into your inventory each turn and allows construction of a Gem Mine to earn much more. Gems are the only way to field Icaroids carrying certain powerful abilities (the full economics are in Economy & Production; what gems actually do is in the glyphs guide).
Deposits are visible on the map no matter your scouting level; they're important strategic targets that can greatly enhance a military's effectiveness, so expect them to be contested.
Strategic fog of war
You can't see the whole map at the start of the game. As you conquer territory and build sight-enhancing structures, you'll gain partial and complete vision over more provinces. Provinces you own are always shown fully; information about the rest is usually guessed or estimated. Strategic sight is calculated along traversal connections, not proximity. Sensor buildings (watchtowers, sensor webs, spires) extend that reach further, some revealing full detail and some only a partial outline.
Fog hides more than just the terrain or economics of a province. Enemy army sizes are estimated: you can see that a hostile force is present and its rough size, but never its exact headcount or composition. Sensor structures give you more accurate intel, so they're worth the investment on a front where you expect - or even suspect - an incoming attack.
Reading the board
Put together, the map can dictate the best place to engage an enemy: defend big provinces and chokepoints, attack or trade small ones, and solidify control over your prized gem deposits. Whatever you do, don't lose your capitol! Next, consider reading up on the Armies & Movement to actually control and conquer territory.