  This master's thesis gives a thorough and pedagogical introduction to the
Dijkgraaf-Vafa conjecture which tells us how to calculate the exact effective
glueball superpotential in a wide range of $\mathcal{N}=\textrm{1}$
supersymmetric gauge theories in four space-time dimensions using a related
matrix model. The introduction is purely field theoretical and reviews all the
concepts needed to understand the conjecture. Furthermore, examples of the use
of the conjecture are given. Especially, we find the one-cut solution of the
matrix model and use this to obtain exact superpotentials in the case of
unbroken gauge groups. Also the inclusion of the Veneziano-Yankielowicz
superpotential and problems such as the nilpotency of the glueball superfield
are discussed. Finally, we present the diagrammatic proof of the conjecture in
detail, including the case where we take into account the abelian part of the
supersymmetric gauge field strength. This master's thesis was handed in May
2004 and appears here with minor changes.
