"At the boundaries of physics research it is constantly necessary to introduce new tools and methods to expand the horizons and address fundamental issues. In this proposal, we will develop and then apply radically new tools that will enable groundbreaking progress in the field of vortex matter in superconductors and will be of great importance to condensed matter physics and nanoscience. We propose a new scanning magnetic imaging method based on self-aligned fabrication of Josephson junctions with characteristic sizes of 10 nm and superconducting quantum interference devices (SQUID) with typical diameter of 100 nm on the end of a pulled quartz tip. Such nano-SQUID on a tip will provide high-sensitivity high-bandwidth mapping of static and dynamic magnetic fields on nanometer scale that is significantly beyond the state of the art. We will develop a new washboard frequency dynamic microscopy for imaging of site-dependent vortex velocities over a remarkable range of over six orders of magnitude in velocity that is expected to reveal the most interesting dynamic phenomena in vortex mater that could not be investigated so far. Our study will provide a novel bottom-up comprehension of microscopic vortex dynamics from single vortex up to numerous predicted dynamic phase transitions, including disorder-dependent depinning processes, plastic deformations, channel flow, metastabilities and memory effects, moving smectic, moving Bragg glass, and dynamic melting. We will also develop a hybrid technology that combines a single electron transistor with nano-SQUID which will provide an unprecedented simultaneous nanoscale imaging of magnetic and electric fields. Using these tools we will carry out innovative studies of additional nano-systems and exciting quantum phenomena, including quantum tunneling in molecular magnets, spin injection and magnetic domain wall dynamics, vortex charge, unconventional superconductivity, and coexistence of superconductivity and ferromagnetism."