1) Menu - Part I
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New,

Open and

Save. INVedit has it's own save format for inventories (.inv), which you can use to save your inventory somewhere else than in a world or to show it to a friend. You won't need these if you want to edit your game inventory.
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Open from game and

Save to game. Click the small arrows to quick-load/save.
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Reload and

Close tab.
2) Inventory tabs. Lists all your open inventories.
3) Item slot. If selected, it has a black rectangle inside.
4) The current damage (uses) and count of the selected item. Those boxes are the only way to edit the damage of an item and its count to something the game wouldn't allow you.
5) Drag items in here to remove them.
6) Group list. Select the groups you want to show in the item list. Right-click to only show the one you clicked.
7) Item list. Drag items out of here and drop them on one of the item slots.
8) Menu - Part II
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Update. This is enabled if one is available.
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About. Displays the "About INVedit" window.