The LDS church was founded by Joseph Smith in the 19th century. Joseph Smith claimed that he was a prophet of God sent to refound the church after it had (allegedly) fallen away in the first century of the Christian era. He claimed an angel named Moroni appeared to him and showed him the location of metal plates, which he said contained records of ancient Israelites who journeyed to the American continent. This he published in 1830 as The Book of Mormon.
Joseph Smith lead his followers to Navuoo?, Illinois. There he introduced the practice of polygamy, or plural marriage. This caused friction between the Mormon and non-Mormon elements elements of the local population. Opponents of Joseph Smith attempted to publish material criticial of him, and when Joseph Smith tried to stop them he was imprisoned, where he was murdered by a mob of anti-Mormons.
After the death of Joseph Smith, the Mormon church fractured. A number of groups developed claiming to be the true Mormon church, e.g. the Strangites. Eventually the church developed into two main factions. The larger, lead by Brigham Young, accepted polygamy and travelled to what is now Utah to found Salt Lake City; the smaller, lead by Joseph Smith's wife and son, rejected polygamy and remained in Navuoo. The smaller faction developed into the Re-organized Church of Latter-day Saints (the RLDS church), while the larger developed into the LDS church.
The RLDS church tends to be more liberal, and closer to mainstream Christianity, than the LDS church.
The Mormon practice of polygamy caused conflict between Mormons and the wider American society, which lead the LDS church leadership to prohibit the practice in 1890. LDS church members today who attempt to marry more than one wife are excommunicated. However small groups of Mormons refused to accept the prohibition of polygamy, and continue to practice it to this day. They are often called [fundamentalist Mormons]?, and have their own churches.
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