Lutetium is a chemical element with the symbol Lu and atomic number 71. It is a silvery white metal, which resists corrosion in dry air, but not in moist air. Lutetium is the last element in the lanthanide series, and it is traditionally counted among the rare earths. Lutetium is generally considered the first element of the 6th-period transition metals by those who study the matter, although there has been some dispute on this point.

Lutetium is not a particularly abundant element, although it is significantly more common than silver in the earth's crust. It has few specific uses. Lutetium-176 is a relatively abundant (2.5%) radioactive isotope with a half-life of about 38 billion years, used to determine the age of minerals and meteorites. Lutetium usually occurs in association with the element yttrium and is sometimes used in metal alloys and as a catalyst in various chemical reactions. 177Lu-DOTA-TATE is used for radionuclide therapy (see Nuclear medicine) on neuroendocrine tumours.

Lutetium has the highest Brinell hardness of any lanthanide, at 890–1300 MPa.