  In the thesis we analize different problems related to the supersymmetric
extension of the Dirac-Born-Infeld action. In chapter 2 we introduce the DBI
action and show how it appears in string theory, we discuss also it's
connection with Dp-branes. Chapter 3 is a self contained introduction to
supersymmetry, with emphasis on BPS states. In chapter 4 we construct the N=2
supersymmetric extension of the Born-Infeld-Higgs in three space-time
dimensions and discuss it's BPS states and Bogomol'nyi bounds. In chapter 5 we
construct the N=1 supersymmetric extension of the non-abelian Born-Infeld
theory in four space-time dimensions. Chapter 6 deals with the analisis of BPS
and non-BPS solutions of the Dirac-Born-Infeld action and their interpretation
in superstring theory. Chapter 7 is devoted to the conclusions. Three appendix
complete the work.
