In this thesis, the problem of equidissectability of polytopes is discussed. After a short introduction of the basic notions, the question of when two polytopes in the plane are equidissectable is completely solved with the Bolyai-Gerwien theorem. After that, a formal criterion for arbitrary dimensions is obtained. In particular, it is shown that two polytopes are equidissectable if and only if they are equicomplementable. Finally, the important Dehn-Sydler theorem, which is a practical characterization for equidissectability in three-dimensional space, is proven. Using this result, a corresponding characterization in four-dimensional space, Jessen's theorem, is obtained.