Materials are necessary for upgrading gears and your ship. Most of them can be found in the wild by harvesting trees, hunting animals, mining from caves and ore deposits, even looted from fallen enemies. Common materials like leather, wood, and iron can be salvaged from dismantled gear.
Materials sources like animals, wild trees, and ore deposits replenish over time so it's possible to come back to the same location after a while and gather them. In the other hand, you'll get a lot of materials by completing War Contracts and Bounties accepted from Message Boards in major towns. These are repeatable quests that give decent EXP but lots of gold and materials, especially important for upgrading higher level gears and unlocking better upgrades for your ship.
Soft Leather
Used to engrave armor, upgrade weapons, armor, and the Adrestia
Primarily earned by hunting animals or recovered from dismantled gear.
Iron Metal
Used to engrave weapons, upgrade weapons, armor, and the Adrestia
Can be mined in caves, looted from soldiers and bandits, or recovered from dismantled gear
Olive Wood
Used to craft arrows, upgrade the Adrestia
Can be salvaged from sinking ships, certain wild trees, or recovered from dismantled gear
Ancient Tablets
Can be used to upgrade the Adrestia
Retrieved from ancient ruins scattered throughout the world.
Take note that some ruins are heavily guarded by hostiles so you may need to clear them as well to mark the location as "Complete"
Precious Gems
Used to upgrade gear
Can be mined from ore deposits inside caves.
Looted from mercenaries.
Earn by completing Bounties
Obsidian Glass
Used to upgrade gear
You may occasionally harvest them alongside iron metal from ore deposits.
Rare volcanic mineral can be looted from Leaders
Loot from Nation Chests in Forts
Complete Contracts and Conquest Battles