There are various ways to repair items in Advent of Ascension.
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Magic Repair Dust/Magic Mending Compound 
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A Mending Table.
By using a Mending Table, the player can repair items by using Magic Repair Dust or Magic Mending Compound via putting them in the middle slot, and putting applicable items in the left slot. Magic Repair Dust will restore an item by 20% of its total durability value, while Magic Mending Compound will restore an item's durability to full. This does not cost any Experience.
This method is compatible with almost any item that has a durability value.
Same-Item Repairing 
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By using an Anvil, Crafting Table or the 2x2 crafting grid in the player's inventory, combining 2 of the same item will combine them into 1, merging their durability values (cannot go above max), along with adding an extra 5% durability. This costs Experience when done in an Anvil, but any enchantments the 2 items have are kept if done in an Anvil.
This method is also compatible with almost any item that has a durability value.
Material Repairing []
By using an Anvil, combining a damaged item with the primary material used to craft it will restore durability. E.G. Putting a damaged Limonite Pickaxe and Limonite Ingot in an Anvil. Doing this restores an item by 25% of its total durability value. This costs Experience to do so.
This method is only compatible with the following items:
Additionally, Crystal Carver can be repaired with any item considered a "gem".