Lutetium is a chemical element; it has 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 earth elements; it can also be classified as the first element of the 6th-period transition metals.

Lutetium was independently discovered in 1907 by French scientist Georges Urbain, Austrian mineralogist Baron Carl Auer von Welsbach, and American chemist Charles James. All of these researchers found lutetium as an impurity in ytterbium. The dispute on the priority of the discovery occurred shortly after, with Urbain and Welsbach accusing each other of publishing results influenced by the published research of the other; the naming honor went to Urbain, as he had published his results earlier. He chose the name lutecium for the new element, but in 1949 the spelling was changed to lutetium. In 1909, the priority was finally granted to Urbain and his names were adopted as official ones; however, the name cassiopeium (or later cassiopium) for element 71 proposed by Welsbach was used by many German scientists until the 1950s.

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.

A lutetium atom has 71 electrons, arranged in the configuration [Xe] 4f¹⁴5d¹6s². Lutetium is generally encountered in the +3 oxidation state, having lost its two outermost 6s and the single 5d-electron. The lutetium atom is the smallest among the lanthanide atoms, due to the lanthanide contraction, and as a result lutetium has the highest density, melting point, and hardness of the lanthanides. As lutetium's 4f orbitals are highly stabilized only the 5d and 6s orbitals are involved in chemical reactions and bonding; thus it is characterized as a d-block rather than an f-block element, and on this basis some consider it not to be a lanthanide at all, but a transition metal like its lighter congeners scandium and yttrium.

Lutetium's compounds almost always contain the element in the +3 oxidation state. Aqueous solutions of most lutetium salts are colorless and form white crystalline solids upon drying, with the common exception of the iodide, which is brown. The soluble salts, such as nitrate, sulfate and acetate form hydrates upon crystallization. The oxide, hydroxide, fluoride, carbonate, phosphate and oxalate are insoluble in water.

Lutetium metal is slightly unstable in air at standard conditions, but it burns readily at 150 °C to form lutetium oxide. The resulting compound is known to absorb water and carbon dioxide, and it may be used to remove vapors of these compounds from closed atmospheres. Similar observations are made during reaction between lutetium and water (slow when cold and fast when hot); lutetium hydroxide is formed in the reaction. Lutetium metal is known to react with the four lightest halogens to form trihalides; except the fluoride they are soluble in water. ^{[citation needed]}

Lutetium dissolves readily in weak acids and dilute sulfuric acid to form solutions containing the colorless lutetium ions, which are coordinated by between seven and nine water molecules, the average being [Lu(H₂O)_8.2]³⁺.

Lutetium is usually found in the +3 oxidation state, like most other lanthanides. However, it can also be in the 0, +1 and +2 states as well.