  This thesis consists of an introductory text, which is divided into two
parts, and six appended research papers. The first part contains a general
discussion on conformal and superconformal symmetry in six dimensions, and
treats how the corresponding transformations act on space-time and superspace
fields. We specialize to the case with chiral (2,0) supersymmetry. A formalism
is presented for incorporating these symmetries in a manifest way. The second
part of the thesis concerns the so called (2,0) theory in six dimensions. The
different origins of this theory in terms of higher-dimensional theories (Type
IIB string theory and M-theory) are treated, as well as compactifications of
the six-dimensional theory to supersymmetric Yang-Mills theories in five and
four space-time dimensions. The free (2,0) tensor multiplet field theory is
introduced and discussed, and we present a formalism in which its
superconformal covariance is made manifest. We also introduce a tensile
self-dual string and discuss how to couple this string to the tensor multiplet
fields in a way that respects superconformal invariance.
