The search for fast growing infinitesimal perturbations in the Friedmann-Lematre-Robertson-Walker universe within Einsteins General Relativity is regarded as very important for explanation of observational inhomogeneities such as nebulae and clusters of galaxies. Chapter One reports on numerical solutions of Hawkings equations for gravitational waves in evolutionary universe, which includes wave-matter interaction. Chapter Two presents an overview of various options of direct including of SQUID into a system for registering effects of super weak elongation or very little force. Chapter Three reviews previous work on constraining gravitational radiation from elliptically deformed pulsars with terrestrial nuclear laboratory data in light of the recent gravitational wave detection, and estimates the maximum gravitational wave strain amplitude, using an optimistic value for the breaking strain of the neutron star crust. Chapter Four explores the LIGO signal GW150914 within the braneworld scenario. Future space flight propelled by artificially-generated Gravitational Wave (GW) beam is discussed within the framework of the General Relativity theory in the final chapter of this book.