During the last thirty years lots of cosmological experimental data has been collected. In order to understand these collected data lots of work has been done in developing various theoretical models of effective Quantum Gravity (QG). In this network we focus on String theory, Noncommutative geometry and effective theories of modified gravity. The Network consists of 9 institutions from 7 countries and 2 silent partners. Two main objectives of the network are: combining different expertise of each node into an effort of constructing realistic theoretical models of effective QG, inflation and cosmology and intensive discussion and first steps towards joint master and PhD programs between the nodes. Main achievements of QSGravCos network will be: extending existing and creating new collaborations, introducing students to this very popular and active field of research and promoting scientific and cultural heritage of each country included in the network.