The One Mukhi Rudraksha is the symbol of UKAR i.e. which is formless, depthless, shadow less, Godhood, Supreme Truth and Attainment of Eternity who has created this entire world.

The one Mukhi Rudraksha belongs to Shiv UKAR and keeps the balance of the entire universe.
"U" can also be understood as Hiranya-Garbha, Shankar-Tejam, Yoga-Darshan and vast(boundless). The wearer of this Rudraksha should meditate on the symbol of " Om". The person who leaves the world while meditating on " Om "; liberates and finds the best destination after death. He gets the opportunity to have darshan of Lord Shiva. This Rudraksha if worn after proper Sidhhi ( method of purification & charging with Mantra); undoubtedly all desires of the wearer will be fulfilled. It is useful in Meditation and gives highest results. It also keeps the mind cool due to its property. It is best suited for Saints and can also be worn by all others. Any followers of Lord Shiva who is poor if wear the one Mukhi Rudraksha; achieves prosperity and all his wishes are fulfilled.

Note : Above details are taken from ancient handwritten text and Guru Mukha. The description is seen in the deep meditation of Lord Shiva by Lord Datta Treya. The mantra are hidden so not mentioned here.

Rules for the Rudraksha: The Wearer of the Rudraksha should chant related Rudraksha Mantra along with Rudraksha Utpatti Mantra (Mantra for the Rudraksha Origin) daily at least 9 times while wearing and removing in the night before going to sleep. More Rules...

1 Mukhi Rudraksha as found in various Puranas:

The One Mukhi Rudraksha is the symbol of Godhood, Supreme Truth and Attainment of Eternity.

The One Mukhi Rudraksha is itself Lord Shankar and it is the main among all Rudrakshas of all faces. It is ruled by the Sun and enlightens the Super Consciousness. It brings the power of Dharana to the wearer meaning the power to concentrate the mind on an object. The wearer of One Mukhi Rudraksha gets his mental structure changed and he begins to feel renunciation from the worldly affairs and naturally inclines towards GOD. His mind begins to concentrate on the Supreme Element that is Partattva Dharana cha jayate Tatprakashnam thus the discoverers of Aatma Tattva must wear One Mukhi Rudraksha.

This is the best of all Rudrakshas. Peace and pleasure abide in the house where One Mukhi Rudraksha is worshipped. The person who worships it obtains not only all the worldly pleasures during his life span but also remains unaffected by them. It is ideal for Doctors.

In the Srimaddevibhagavat 11th Skand Chapter V verses 25 and 26 it is stated " According to Jabala instinct for wearing Rudraksha results only after attaining the perfection of Vedas and blessings of Lord Siva during preceding births "

In Chapter VII verse 23 it is stated " Rudrakshas infused with Bija mantras should be worn. One Mukhi Rudraksha helps envisioning the Partattva "

In Padma Purana Chapter 57 Translated by Bhatta 1989 it is stated in verse 38 to 39 " The Rudraksha of one mouth is virtually Siva It removes the sin of brahmanacide. Therefore one should wear it for the destruction of all ( ones ) sins. He would go to Siva's heaven and rejoice with Siva. O Kartikeya a man would obtain a Rudraksha of one mouth due to great religious merit and due to Siva's favour and would also obtain Kailasa "

One Mukhi Rudraksha is found in two shapes round and the half moon shape. Round Rudraksha is highly praised in our ancients texts but it is very rare and more of a myth . One Mukhi Half moon is easily available and found in a family tree of Rudraksha from India and Srilanka.From the point of view of importance there is no difference between them. Therefore it must be real and pure in whatever shape it may be. The cost of One Mukhi Round is more than the half moon shaped Rudraksha.