Melchizedek Priesthood

In Mormonism, the Melchizedek priesthood is one of the two or three types, or "orders" of priesthood. The Melchizedek priesthood is also referred to as the high priesthood of the holy order of God (Alma 4:20, 13:8), or the Holy Priesthood, after the Order of the Son of God (LDS D&C 107:3), or simply as the high priesthood. In Mormonism, unlike most other Christian religions, the Melchizedek priesthood is thought to be held by mortals as a normal priesthood office, and not solely by either pre-Aaronic priests such as Melchizedek, or Jesus alone, as most Christians interpret the Epistle to the Hebrews. This priesthood is named after Melchizedek "because Melchizedek was such a great high priest." (D&C 107:2)

The Melchizedek priesthood in The Church of Jesus Christ of Latter-day Saints
In The Church of Jesus Christ of Latter-day Saints, the largest denomination of Mormonism, the Melchizedek priesthood is one of two recognized priesthoods, which is usually given as a matter of course to worthy members 18 years and older who have been a member of the church for over one year. Ordination is based on the recipient's age, gender, and moral worthiness without regard to training, knowledge, or aptitude.

Presidencies
Each quorum and organizational unit in the church has a presidency attached to it. A presidency is composed of three members: the president and two counselors. Typically, a president is selected and he chooses the two counselors whom he would like to serve with him. On very rare occasions there may be only one counselor or three counselors. Usually, a secretary is also called by the president to serve, but he is not considered a part of the presidency by authority. Each of the counselors is given a precedence, for instance, "first counselor" and "second counselor".

The one exception to this precedent is in the Presidency of the Seventy, which consists of seven presidents equal in authority.

The counselors serve under the direction of the president and share in his responsibilities. The president may assign each counselor to handle certain areas of responsibility. The president bears the sole burden of being the final arbiter of decisions, but he is advised to counsel with his advisors and pay close attention to their advice and insight.

When the president is released, the counselors are released as well.

A bishopric is organized much like a presidency, except the president is the bishop.

Priesthood Leadership callings
In addition to the regular offices of the Aaronic or Melchizedek Priesthood referred to in the chart above, there are other leadership callings within the Aaronic and Melchizedek Priesthoods. The table below lists these other Priesthood leadership callings and the table below it shows how the various callings are organized within the hierarchy of the Church.

Hierarchy
Area Presidencies: Presidents and 1st and 2nd Counselors are filled by Seventies Local Authorities Third, Fourth, Fifth, Sixth, and Seventh Quorums of the Seventy (Area Authority Seventies) Temple Presidencies Stake Presidencies and High Councils Mission Presidencies Ward Bishoprics or Branch Presidencies Elder Quorums High Priest Groups   Deacon Quorums Teacher Quorums Priest Quorums