For the past few decades physicists have used the tools of quantum field theory to study the high energy, small-scale structure of the universe. Two promising candidates, string theory and supersymmetry, have also emerged as possible essential ingredients of a unified theory of all fundamental interactions. Most of our understanding of these areas has been obtained using perturbation theory which by construction is a largely incomplete description of a quantum theory. Many of the outstanding questions in theoretical physics such as the dynamics of quarks inside a nucleus, the full quantum nature of black holes, or the origin of our 4-dimensional spacetime will probably be answered only when we have complete non-perturbative formulations of the theories that we use to study them.

What is remarkable is that much of the recent progress in understanding non-perturbative aspects of string theory and supersymmetric gauge theories has been made in parallel, using each to gain knowledge and insights about the other. There are various reasons for this intimate connection between supersymmetric gauge theories and string theory. One is that supersymmetric gauge theories arise as low energy effective descriptions of compactified string theories in limits where gravity decouples. Another reason is that superstring theories can be formulated in backgrounds that contain D-branes, and supersymmetric gauge theories serve as effective world volume theories for these D-branes. In addition to these direct examples, it is sometimes the case that intuition about non-perturbative physics that is gained in one area can be directly applied to the other. An example of this is the guiding principle that singularities in the quantum moduli space of a low energy effective theory signal the appearance of new massless states. This was seen to be a generic phenomena in supersymmetric gauge theories and was subsequently applied to the resolution of conifold singularities by massless black holes in string theory.

What has become clear is that by studying the seemingly
disparate subjects of string theory, supergravity, and supersymmetric gauge
theories we are uncovering aspects of a single underlying theory.
Each description has a separate regime of validity corresponding to different
limits in the moduli space of the underlying theory.

The main challenge for the future is to precisely define
this fundamental theory, and to show that it naturally leads to the observed
physics of our universe.

In this dissertation we study some non-perturbative aspects
of *N = 1* and *N = 2* supersymmetric
gauge theories and the physics of branes in the context
of string theory, M-theory, and black holes
in supergravity. In Chapter II, we discuss exact
non-perturbative results in *N = 1* supersymmetric
gauge theories with exceptional gauge groups. Theories
with $N=1$ supersymmetry (such as the Minimal Supersymmetric Standard
Model) are widely believed to be relevant to describing
physics at energies above the TeV
scale. Exceptional gauge groups are of interest
because they naturally appear in string theory and *E _{6}*,
for example, may hold promise as a grand unified gauge
group. Beyond that, it is hoped that by studying
many examples we may learn something new about the
strong coupling dynamics of gauge theories such as
new phases, new mechanisms for dynamical supersymmetry
breaking, identifying generic properties, and uncovering
the fundamental concepts behind duality. We treat
the case with gauge group

In Chapter III, we study the *N
= 2* supersymmetric gauge theory with gauge group *G _{2}*.

In Chapter IV, we move on to string theory and M-theory.
String theories are of great interest because they are
consistent theories of quantum gravity and they have the
potential to reproduce the gauge group and matter
content of the Standard Model at low energies.
The five known superstring theories
in ten dimensions are linked together by various dualities,
which include a phase in which an eleventh dimension opens up. This
phase, known as M-theory, arises as the strong coupling
limit of the IIA and *E _{8} x E_{8}* heterotic
string theories. It has eleven
dimensional supergravity as its low energy effective theory,
and in some sense can be thought of as the most symmetric
phase. We discuss the matrix formulation of
M-theory also known as M(atrix) theory, which is conjectured
to be a full quantum description of M-theory
in the infinite momentum frame. We review the relationship between
the various BPS p-branes in IIA string theory and
its eleven dimensional M-theory limit and study the
scattering of these branes in string theory and M(atrix)
theory, concentrating mainly on the interactions of
eight-branes.

In Chapter V, we use D-branes to probe
a black hole which carries 0- and 6-brane charge and
examine its relationship to a possible bound state
configuration of D0-branes and D6-branes. An
appropriate configuration of D-branes can provide
a weakly coupled microscopic description of a black hole which
is intrinsically a strongly-coupled macroscopic object. Black
holes serve as useful theoretical laboratories in which to
test the effects of a quantum theory of gravity such as string
theory. We show that the long distance interactions
between the supergravity black hole and p-brane probes
are exactly reproduced using the D-brane configuration
and string theory.