  This thesis provides an explicit, general trace formula for the Hecke and
Casimir eigenvalues of GL(2)-automorphic representations over a global field.
In special cases, we obtain Selberg's original trace formula. Computations for
the determinant of the scattering matrices, the residues of the Eisenstein
series, etc. are provided. The first instance of a mixed, uniform Weyl law for
every algebraic number field is given as standard application. "Mixed" means
that automorphic forms with preassigned discrete series representation at a set
of real places are counted. "Uniform" indicates that the estimates implicitly
depend on the number field, but not on the congruence subgroup. The method of
proof relies on a suitable partition of the cuspidal, automorphic spectrum, and
the explication of the non-invariant Arthur trace formula via Bushnell and
Kutzko's theory of types. A pseudo matrix coefficient for each local,
square-integrable representation, i.e., the discrete series, the supercuspidal,
or the Steinberg representation, is constructed explicitly.
