  In addition to the conventional $q\bar{q}$ and $qqq$ bound states of quarks
$q$, exotic hadrons, such as the four-quark $q\bar{q}q\bar{q}$ and the
five-quark $qqqq\bar{q}$ bound states, can be constructed by assuming colour
confinement in strong interactions. In particular, one of the possible internal
structure for a four-quark state is the tetraquark $[qq][\bar{q}\bar{q}]$,
where diquarks $[qq]$ and antidiquarks $[\bar{q}\bar{q}]$ are bound due to the
colour force. In this thesis, heavy-light $[Qq]$, where $Q\in\{c, b\}$ (charm,
bottom) and $q\in\{u,d,s\}$ (up, down, strange), and doubly-strange $[ss]$
diquarks are examined using QCD Laplace sum-rules. The diquark two-point
correlation function is renormalized using diagrammatic renormalization methods
for QCD correlation functions that are developed and compared to the
conventional renormalization method. It is shown that the mixing of composite
operators induced by the conventional renormalization approach is avoided by
the diagrammatic renormalization method. The strange quark condensate parameter
$\kappa=\langle\bar{s}s\rangle/\langle\bar{n}n\rangle$, where $n\in\{u,d\}$, is
shown to have an important role on the $[Qs]$ and $[Qn]$ diquark mass
splitting.
