Transmute Formula 3 Perfect Skulls + 1 Rare Item + Stone of Jordan = Add 1 Socket To a Rare Item
Rare Items can only have one socket. You cannot add sockets to items that don't normally have sockets. You can not use this on a Rare with one socket. You can only add one socket to a zero socket Rare Item.

Transmute Formula 3 Standard Gems (normal) and 1 Socketed Weapon (Any Type) = 1 Socketed Magic Weapon (of same type)
This takes a socketed weapon and makes it a magic socketed weapon with a random number of sockets. This allows you to get new magic bonuses on an otherwise non magical weapon. The original weapon properties will be removed (rerolled) when the new weapon is created. ilvl = 30. It gets 1-2 sockets.

Transmute Formula 3 Chipped Gems + 1 Magic Weapon = Socketed Magic Weapon
This adds sockets to a magic weapon. The original magic weapon properties will be removed (rerolled) when the new weapon is created. If you use this formula with a weapon that is not normally socketed such as a Javelin, this recipe will create a new magical weapon without any sockets. ilvl=25 magic weapon with 1-2 sockets.

Transmute Formula 3 Flawless Gems + 1 Magic Weapon = Socketed Magic Weapon
This adds sockets to a magic weapon. The original magic weapon properties will be removed (rerolled) when the new weapon is created. If you use this formula with a weapon that is not normally socketed such as a Javelin, this recipe will create a new magical weapon without any sockets. ilvl=30 magic weapon with 1-2 sockets.

Transmute Formula 1 Tal Rune + 1 Thul Rune + 1 Perfect Topaz + Normal Body Armor = Socketed Body Armor of same type
The number of sockets created will vary. The item must be normal and unsocketed. Low-quality items and superior items do not work. The item gets 1-4 sockets, randomly. However, the number of sockets is then restricted by the maximum number of sockets that base item with that ilvl can have. The chance to get X sockets in most armor is 1/4 (I.E: Mage plate has a max of 3 sockets, so it has a 2/4 [1/2] chance to get 3 sockets). The base of 6 was used in the ratios for all the above mentioned areas.

Transmute Formula 1 Ral Rune + 1 Amn Rune + 1 Perfect Amethyst + Normal Weapon = Socketed Weapon of same type
The number of sockets created will vary. The item must be normal and unsocketed. Low-quality items and superior items do not work. The item gets 1-6 sockets, randomly. However, the number of sockets is then restricted by the maximum number of sockets that base item with that ilvl can have. For example, if you have an item that can only have 2 sockets, there's a 5/6 chance of getting 2 sockets and a 1/6 chance of getting 1 socket.

Transmute Formula 1 Ral Rune + 1 Thul Rune + 1 Perfect Sapphire + Normal Helm = Socketed Helm of same type
The number of sockets created will vary. The item must be normal and unsocketed. Low-quality items and superior items do not work. The item gets 1-3 sockets, randomly. However, the number of sockets is then restricted by the maximum number of sockets that base item with that ilvl can have. For example, if you have an item that can only have 2 sockets, there's a 2/3 chance of getting 2 sockets and a 1/3 chance of getting 1 socket.

Transmute Formula 1 Tal Rune + 1 Amn Rune + 1 Perfect Ruby + Normal Shield = Socketed Shield of same type
The number of sockets created will vary. The item must be normal and unsocketed. Low-quality items and superior items do not work. The item gets 1-4 sockets, randomly. However, the number of sockets is then restricted by the maximum number of sockets that base item with that ilvl can have. For example, if you have an item that can only have 2 sockets, there's a 3/4 chance of getting 2 sockets and a 1/4 chance of getting 1 socket.

Transmute Formula 1 Hel Rune + Scroll of Town Portal + Any Socketed Item = Remove items from sockets
Warning: This will destroy any gems, runes, or jewels you have socketed. This is useful if you are not happy with the gems you have socketed and you want to socket the item in another way.