On the Quantitative Subspace Theorem

In this survey we give an overview of recent developments on the Quantitative Subspace Theorem. In particular, we discuss a new upper bound for the number of subspaces containing the "large" solutions, obtained jointly with Roberto Ferretti, and sketch the proof of the latter. Further, we prove a new gap principle to handle the "small" solutions in the system of inequalities considered in the Subspace Theorem. Finally, we go into the refinement of the Subspace Theorem by Faltings and Wuestholz, ...