Chokhmah usually has four paths going to Keter, Binah, Tiphereth and Chesed. Some Kabbalists place a path between Chokhmah and Gevurah.
In Jewish mysticism, it denotes the first intermediate step between Keter and the rest of the sephirot, channelling Or Ein sof through the rest of them.
Chokhmah is the first power of conscious intellect within Creation, and corresponds to tzelem Elokim ("the Divine Image") and the right hemisphere of the brain.
In its highest form, Chokhmah possesses two partzufim ("faces" or "features"): the higher of these is referred to as Abba Ila'ah ("the higher father"), whereas the lower is referred to as Yisrael Saba ("Israel the Elder"). United, these partzufim are referred to as Abba ("father").
In the soul, Chokhmah is associated with the power of intuitive insight; the feeling one gets with "aha!" or "eureka" moments when insight zaps across consciousness like a bolt of lightning. Wikipedia: " The partzufim Abba Ila'ah is associated with the power to spontaneously extract such insight from the superconscious realm, whereas the partzufim of Yisrael Saba is associated with the power to subsequently direct it into consciousness.
The "wisdom" of Chokhmah also implies the ability to look deeply at some aspect of reality and abstract its conceptual essence till one succeeds in uncovering its underlying axiomatic truth. These seeds of truth can then be conveyed to the companion power of Binah for the sake of intellectual analysis and development.
The word Chokhmah itself may be broken into two words- koach ("potential") and ma ("what is"). Thus Chokhmah means "the potential to be." This aspect of Chokhmah describes the state of Chokhmah in relation to the sefira of Keter. As Chokhmah emanates from Keter, the first dawning of the "Infinite Light", as it "appears" in an obscure and undefined state that is a virtual non-being. Thus the verse states, "and Chokhmah emerges from nothingness" (Job 28:12, see Zohar II, 121a, Zohar III, 290a, commentaries). The light of the Ein Sof becomes unified in the world of Atzilut though clothing itself first in the sefira of Chokhmah.
Chokhmah is related to the phallus and the straight line. It is variously attepted to relate it to different chakras in Indian mysticism. One attempt at reconciliation is that both Chokhmah and Binah are united in the Ajna chakra, which is where both Shiva and Shakti, subject and object are united.
In Aleister Crowley's Liber 777, Chokhmah is represented as The Four twos of the Tarot, Illuminating, Thoth, Vishnu, Joy, Odin, Uranus, Athena, God the Father, Man, Amaranth, VIAOV, Star Ruby, Lingam, Hashish, Phosphorus, Musk, and Yang (not a complete list).
Its opposite or Qlippothic equivalent has the name Chaigidel."