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This thesis is dedicated to the study of the geometry of six-dimensionalsuperspace, endowed with the minimal amount of supersymmetry. In the first partof it, we unfold the main geometrical features of such superspace by solvingcompletely the Bianchi identities for the constrained superspace torsion, whichallow us to determine the full six-dimensional derivate superalgebra. Next, theconformal structure of the supergeometry is considered. Specifically, it isshown that the conventional torsion constraints remain invariant undersuper-Weyl transformations generated by a real scalar superfield parameter. Inthe second part of this work, the field content and superconformal mattercouplings of the supergeometry are explored. The component field content of theWeyl multiplet is presented and the question of how this multiplet emerges insuperspace is addressed. Finally, the constraints that conformal invarianceimposes on some matter representations are analyzed.

The Geometry of 6D, N = (1,0) Superspace and its Matter Couplings