Level Truncation Approach to Open String Field Theory

Given a D-brane background in string theory (or equivalently boundary conditions in a two dimensional conformal field theory), classical solutions of open string field theory equations of motion are conjectured to describe new D-brane backgrounds (boundary conditions). In this thesis we study these solutions in the bosonic open string field theory using the level truncation approach, which is a numerical approach where the string field is truncated to a finite number of degrees of freedom. We start with a review of the theoretical background and numerical methods which are needed in the level truncation approach and then we discuss solutions in several different back- grounds. First we discuss universal solutions, which do not depend on the open string back- ground, then we analyze solutions of the free boson theory compactified on a circle or on a torus, then marginal solutions in three different approaches and finally solutions in theories which in- clude the A-series of Virasoro minimal models. In addition to known D-branes, we find so-called exotic solutions which potentially describe yet unknown boundary states.