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The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.

Unitary groups. --- Trace formulas. --- Representations of groups. --- Automorphic forms. --- Abelian group. --- Abuse of notation. --- Addition. --- Admissible representation. --- Algebraic closure. --- Algebraic group. --- Algebraic number field. --- Asymptotic expansion. --- Automorphism. --- Base change map. --- Base change. --- Bijection. --- Borel subgroup. --- Cartan subgroup. --- Class function (algebra). --- Coefficient. --- Combination. --- Compact group. --- Complementary series representation. --- Complex number. --- Congruence subgroup. --- Conjugacy class. --- Continuous function. --- Corollary. --- Countable set. --- Diagram (category theory). --- Differential operator. --- Dimension (vector space). --- Dimension. --- Discrete spectrum. --- Division algebra. --- Division by zero. --- Eigenvalues and eigenvectors. --- Embedding. --- Equation. --- Existential quantification. --- Finite set. --- Fourier transform. --- Fundamental lemma (Langlands program). --- G factor (psychometrics). --- Galois group. --- Global field. --- Haar measure. --- Hecke algebra. --- Homomorphism. --- Hyperbolic set. --- Index notation. --- Irreducible representation. --- Isomorphism class. --- L-function. --- Langlands classification. --- Linear combination. --- Local field. --- Mathematical induction. --- Maximal compact subgroup. --- Maximal torus. --- Morphism. --- Multiplicative group. --- Neighbourhood (mathematics). --- Orbital integral. --- Oscillator representation. --- P-adic number. --- Parity (mathematics). --- Principal series representation. --- Quaternion algebra. --- Quaternion. --- Reductive group. --- Regular element. --- Remainder. --- Representation theory. --- Ring of integers. --- Scientific notation. --- Semisimple algebra. --- Set (mathematics). --- Shimura variety. --- Simple algebra. --- Smoothness. --- Special case. --- Stable distribution. --- Subgroup. --- Summation. --- Support (mathematics). --- Tate conjecture. --- Tensor product. --- Theorem. --- Trace formula. --- Triangular matrix. --- Unitary group. --- Variable (mathematics). --- Weight function. --- Weil group.