Ernest Borisovich Vinberg (Russian: Эрнест Борисович Винберг; born 26 July 1937) is a Russian mathematician, who works on discrete subgroups of Lie groups and representation theory. He introduced Vinberg's algorithm and the Koecher–Vinberg theorem.
He is a recipient of the Humboldt Prize. He is on the executive committee of the Moscow Mathematical Society. In 1983 he was an Invited Speaker with a talk on Discrete reflection groups in Lobachevsky spaces at the International Congress of Mathematicians in Warsaw. In 2010 he was elected a member of the American Academy of Arts and Sciences.
- Linear representations of groups. Birkhäuser, 1989
- A Course in Algebra. American Mathematical Society (AMS), 2003
- editor and co-author: Lie groups and invariant theory. AMS, 2005 (contains Construction of the exceptional simple Lie algebras)
- with A. L. Onishchik: Lie groups and algebraic groups. Springer, 1990; 2012 pbk edition
- with V.V. Gorbatsevich, A.L. Onishchik: Foundations of Lie groups and Lie transformation groups. Springer, 1997
- Hyperbolic reflection groups. Russian Mathematical Surveys, no. 40, 1985, pp. 31–75
- (ed.) Geometry II. Encyclopedia of Mathematical Sciences, Springer 1991, (contains : Vinberg et alia: Geometry of spaces of constant curvature, Discrete groups of motions of spaces of constant curvature)
- Berg, Michael (21 February 2011). "Review of Linear Representations of Groups by Ernest B. Vinberg". MAA Reviews, Mathematical Association of America.