“The most basic principles of the gospel are sometimes those least understood.” Theodore M. Burton
The following information was obtained by searching through numerous LDS books and choosing a few definitions that caught my eye. Please feel free to add to what I’ve provided.
1. The Gospel of Jesus Christ is perhaps the most comprehensive subject that we can study…it embraces all truth, wherever found, in all the works of God and man that are visible or invisible to mortal eyes…revealed and…unrevealed, whether religious, political, scientific, or philosophical…
2. Even though Latter-day Saints use the term “gospell” in several ways, including traditional Christian usages, the Book of Mormon and other latter-day scriptures define it precisely as the way or means by which an individual can come to Christ.
As these two definitions point out the word “gospel” can be used in many ways by church members.
In the churches guide for missionaries, Preach My Gospel, the following definition appears on page 5 (I’ve organized the layout differently).
The Savior defined His gospel to include some very vital and basic doctrines:
1. He came into the world to do His Father’s will, and His Father sent Him into the world to be lifted up on the cross
2. By His Atonement and Resurrection, all men will be lifted up to stand before Christ to be judged of their works, whether they be good or evil
3. Those who exercise faith in Christ, repent of their sins, and are baptized in Christ’s name can be sanctified by the Holy Ghost
4. If they endure to the end, they will stand spotless before Christ at the last day and will enter into the rest of the Lord. Christ will hold them guiltless before the Father. He will be their Mediator and Advocate
5. Those who do not endure in faithfulness to the end will be “cast into the fire . . . because of the justice of the Father.”
(See 3 Nephi 27:13-22; compare 2 Nephi 31:10-21, 3 Nephi 11:31-41; D&C 76:40-42, 50-53.)
Doctrine of Christ
The terms gospel, and the doctrine of Christ are used interchangeably. I personally like to use the doctrine of Christ because it quickly narrows down the topic to the first principles and ordinances of the gospel—which are:
1. Faith in the Lord Jesus Christ
3. Baptism by immersion for the remission of sins
4. Laying on of hands for the gift of the Holy Ghost
Nephi speaking of the doctrine of Christ said, “… my beloved brethren, this is the way; and there is none other way nor name given under heaven whereby man can be saved in the kingdom of God. And now, behold, this is the doctrine of Christ, and the only and true doctrine of the Father, and of the Son, and of the Holy Ghost, which is one God, without end. Amen.” (2 Nephi 31:21)
Nephi speaking to those who follow Christ said, “ye have not come thus far save it were by the word of Christ with unshaken faith in him, relying wholly upon the merits of him who is mighty to save. (2 Nephi 31:19)
“If men were duty to consider themselves, and turn their thoughts and reflections to the operations of their own minds, they would readily discover that it is faith, and faith only, which is the moving cause of all action in them; that without it both mind and body would be in a state of inactivity, and all their exertions would cease, both physical and mental… And as faith is the moving cause of all action in temporal concerns, so it is in spiritual…It is the assurance of things hoped for, the evidence of things not seen (Heb. 11:1); that is, it is the assurance we have of the existence of unseen things.”
“Repentance is the process by which humans set aside or overcome sins by changing hearts, attitudes, and actions that are out of harmony with God’s teachings, thereby conforming their lives more completely to his will. In the words of one latter-day prophet, repentance is “to change one’s mind in regard to past or intended actions or conduct”…Though repentance is indispensable to eternal salvation and to earthly happiness, it is not sufficient by itself to reunite a person with God. Complete repentance first requires faith in the Lord Jesus Christ, which in turn generates strong motivation and power to repent. Both are necessary for, and thus must precede, baptism, the reception of the gift of the Holy Ghost, and membership in the Lord’s kingdom.”
“The meaning of repentance is not that people be punished, but rather that they change their lives so that God can help them escape eternal punishment and enter into his rest with joy and rejoicing. If we have this understanding, our anxiety and fears will be relieved…In our repentance, we should remember that the Lord does not punish us for our sins; he simply withholds his blessings. We punish ourselves. The scriptures tell us again and again that the wicked are punished by the wicked…Jesus Christ has paid for your sin and has thus satisfied justice. Therefore, he will extend mercy to you-if you repent. True repentance on your part, including a change in your life-style, enables Christ, in mercy, to forgive your sin…As long as we dwell on sin or evil and refuse to forgive ourselves, we will be subject to return again to our sins”.
Remission of Sins
“You might as well baptize a bag of sand as a man, if not done in view of the remission of sins and getting of the Holy Ghost. Baptism by water is but half a baptism, and is good for nothing without the other half-that is, the baptism of the Holy Ghost”.
“We sometimes speak of baptism for the remission of sins. The remission, if you will read the scriptures carefully, comes through the baptism of fire and of the Holy Ghost.” 
“Sins are remitted not in the waters of baptism, as we say in speaking figuratively, but when we receive the Holy Ghost… The baptism of the Holy Ghost is the baptism of fire.”
 Gospel Through the Ages by Milton R. Hunter, p. 2-3.
 Encyclopedia of Mormonism, p. 556.
 Lectures on Faith, Lecture First.
 Encyclopedia of Mormonism, p. 1216-17
 Theodore M. Burton, “The Meaning of Repentance,” Ensign, Aug 1988, 6-9
 History of the Church, 5:499
 What Every Member Should Know,” Ensign, Aug 2006, 46–52
 New Witness for the Articles of Faith, Bruce R. McConkie, p. 290