Lessons 8-9: Restoration of the priesthood, and organization of the Church

Current priesthood organization
(For the benefit of young women or newer members or long-time members who are still confused about the whole thing.)

Aaronic Priesthood offices
Deacon [12+] (DQ president is from their own quorum)
Teacher [14+] (TQ president is from their own quorum)
Priest [16+] (PQ president is the bishop)

Melchizedek Priesthood offices
Elder (EQ president from their own quorum)
High Priest (HPQ president is the stake president -- that's why ward's have high-priest groups
Patriarch (forgot about this in class, not sure if there's a quorum, but it is an office in the Melchizedek Priesthood)
Seventy (used to be a stake-level office/calling, now it's an area/general authority-level calling; BTW the 1st and 2nd Quorums of Seventy are general authorities -- the 3rd through 8th are area authorities; as needed more of the area-authority quorums of seventy will be added as the church grows)
Apostle (usually only 12 in the Quorum of Twelve Apostles, plus three in the First Presidency; the one who has been in the Quorum the longest [not the oldest!] traditionally becomes the next president of the Church; the new president traditionally chooses his counselors from the other Quorum members to create a new First Presidency; all 15 of these men are referred to as prophets, seers, and revelators -- the entire Church sustains them as such every April in General Conference)

It Will Fill the World
Wilford Woodruff records: “In April of 1834, I arrived, a newly baptized member in Kirtland, Ohio. It was the first time I have ever seen the Prophet Joseph Smith and he invited me home with him. The next evening the Prophet called on all who held the Priesthood to gather into a little log school house. It was small, perhaps 14 feet square, but it held the whole of the priesthood of the Church of Jesus Christ who were then in Kirtland. That was the first time I had ever seen Oliver Cowdery or heard him speak. The first time I ever seen Brigham Young and Heber C. Kimball. The Prophet called upon those present to bear testimony of this work. Those I had named spoke as well as many others. When they got through the Prophet said:

'Brethren, I have been very much edified and instructed in your testimonies here tonight, but I want to say to you before the Lord, that you know no more concerning the destinies of this Church and kingdom than a babe upon its mother’s lap. You don’t comprehend it. It is only a little handful of Priesthood you see here tonight, but this Church will fill North and South America—it will fill the world.'"

(Wilford Woodruff, in Conference Report, Apr. 1898, p. 57).

The Standard of Truth
"The Standard of Truth has been erected; no unhallowed hand can stop the work from progressing; persecutions may rage, mobs may combine, armies may assemble, calumny may defame, but the truth of God will go forth boldly, nobly, and independent, till it has penetrated every continent, visited every clime, swept every country, and sounded in every ear, till the purposes of God shall be accomplished and the Great Jehovah shall say the work is done" (Joseph Smith Jr., History of the Church 4:540).

This statement is the closing paragraph of the Wentworth Letter, which is also the source of our 13 Articles of Faith.