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Versatile chemical transformations of surface functional groups in two-dimensional transition-metal carbides (MXenes) open up a previously unexplored design space for this broad class of functional materials. We introduce a general strategy to install and remove surface groups by performing substitution and elimination reactions in molten inorganic salts. Successful synthesis of MXenes with oxygen, imido, sulfur, chlorine, selenium, bromine, and tellurium surface terminations, as well as bare MXenes (no surface termination), was demonstrated. These MXenes show distinctive structural and electronic properties. For example, the surface groups control interatomic distances in the MXene lattice, and Ti_n+1C_n(n= 1, 2) MXenes terminated with telluride (Te²⁻) ligands show a giant (>18%) in-plane lattice expansion compared with the unstrained titanium carbide lattice. The surface groups also control superconductivity of niobium carbide MXenes.