Aspects of Born-Infeld Theory and String/M-Theory

These notes provide a hopefully pedagogic introduction to Born-Infeld theory and some of its uses in String/M-Theory from the perspective of some-one interested in spacetime geometry. Causality and the consequences of having both the open string and closed string metric are stressed. This leads to some new insighst into old problems, such as strings at finite temperature. Various strong coupling limits of both Born-Infeld and the M5-brane theories are described and their relevance for tachyon condensations are mentioned.Comment: 29 pages plain Latex. Written version of lectures delivered, amongst other places, at the 37th Karpacz School on Theoretical Physics and the 4th Mexican School on Gravitation and Mathematical Physic