  The most prominent class of integrable quantum field theories in 1+1
dimensions is affine Toda theory. Distinguished by a rich underlying Lie
algebraic structure these models have in recent years attracted much attention
not only as test laboratories for non-perturbative methods in quantum field
theory but also in the context of off-critical models. After a short
introduction the mathematical preliminaries such as root systems, Coxeter
geometry, dual algebras, q-deformed Coxeter elements and q-deformed Cartan
matrices are introduced. Using this mathematical framework the bootstrap
analysis of the affine Toda S-matrices with real coupling is performed and
several universal Lie algebraic formulae proved. The Lie algebraic methods are
then extended to define a new class of colour valued S-matrices and also here
universal expressions are derived. The second part of the thesis presents a
detailed analysis of the high-energy regime of the integrable models discussed
in the first part. By means of the thermodynamic Bethe ansatz the central
charges of the ultraviolet conformal field theories are calculated and in case
of affine Toda theories also the first order term in the scaling function is
analytically obtained. For the colour valued S-matrices the connection to WZNW
coset models is discussed. A particular subclass of them, the so-called
Homogeneous Sine-Gordon models, is investigated in some detail and it is found
that the presence of unstable particles in these theories gives rise to a
staircase pattern in the corresponding scaling function. This thesis summarizes
the results of previously published articles listed in the introduction.
