From the very start, neutron interferometer experiments have been established as an ideal technique for the investigation of foundations of quantum mechanics with massive particles: in particular, those experiments, where interference effects of matter waves are involved, have served as elegant demonstrations related to quantum mechanical phenomena. This technique enabled to perform many text-book experiments of quantum physics such as demonstrations of 4π spinor symmetry of neutron’s 1/2-spin, spin superposition, gravitationally induced phase and non-inertial motional effects. In addition, an alternative method using neutron polarimeters was developed to make phase measurements, like topological phase measurements, possible particularly in cases where high stability and efficiency are called for. In this project, following our recent development of implementation of triple entanglement in a single-neutron system, we propose three major research targets: (i) Detailed study and further implementation of various type of double entanglement in neutrons as well as their application for studies of decoherence phenomena (ii) Detailed study and further implementation of a variety of triple entanglement in neutrons (iii) Implementation of quadruple entanglement in neutrons In a previous project “Neutron interferometric and polarimetric investigation of quantum mechanical phenomena” (June 2005 - May 2008), we accomplished the first experimental demonstration of a triply entangled GHZ state implemented in neutrons. We now have rather realistic and concrete proposals of further investigations of the three major subjects above. And, by appropriately developing some needed optical elements, we consider that the realizations of the experiments are in sight. It is worth noting that, since the entanglement of subspaces in single-particles, in particular with the use of a polarimeter setup, are easily applicable for other system than neutrons, the obtained achievements are widely valid. In all cases experimental investigation will have priority and theoretical support will be provided from collaborations with other groups, in Austria and worldwide. The aim of the project is to contribute also to the impressive progress of quantum optics and quantum information/communication technology by the use of the specific properties of neutrons as an elementary matter wave system.