The Radical Republicans, a faction of the Republican Party that existed around the time of the Civil War, believed in the unconditional abolition of slavery and the punishment of those who engaged in the practice. They felt Lincoln took a too conservative approach to the war and advocated for more vigorous military activity. They also opposed the compensation of former slave owners and voted for harsh Reconstruction plans.
One of the chief differences between the Radicals and moderate Republicans like Lincoln was in their views on readmittance of slave states to the Union. While Lincoln favored a plan that required only 10 percent of a former Confederate state's population to swear fealty to the Union and abide by emancipation, the Radicals demanded a majority of the population take an "ironclad oath" that they had never supported the Confederacy and that anyone who refused be denied the right to vote. They also wanted to disband the plantation system, redistribute land and guarantee civil rights for former slaves.
Outside of the slavery question, the beliefs of Radical Republicans were varied. The party was a single-issue party and attracted former Whigs, Democrats and members of many different groups. This diversity of political opinion helped keep the group disorganized and led to their eventual collapse in the 1870s.