"Interaction of extreme&controlled light fields with matter is driving an ongoing revolution in our understanding of quantum physics. Controlled—pulsed—visible lasers have enabled time-dependent two-dimensional (2D) spectroscopy currently transforming chemistry, and led to key milestones such as frequency combs.Despite progress on coherent soft- and hard-x-ray pulsed sources during the last 10 years—e.g. x-ray free-electron lasers (FELs) or high-harmonic generation of laser light, nonlinear (e.g. 2D) spectroscopy or phase control of x-ray light remained a major challenge.Here, I propose to experimentally realize- (a) x-ray two- and multi-dimensional spectroscopy- (b) resonant gain without inversion and spectral control of x raysfor the scientific goals- (a) time- and quantum-state-resolved measurement of fundamental few- and many-electron dynamics- (b) generation of soft-(electronic) and hard-x-ray (nuclear) frequency combsFor (a), a 4-quadrant x-ray time-delay unit will generate coherently-timed pulses out of one spatially coherent beam. For (b) a new physical mechanism relating Fano to Lorentz resonances and absorption to gain by a single temporal phase will be harvested.Scientific impact:(a): Site-specific 2D-x-ray spectroscopy will phase-sensitively test&promote theory and allow to understand fundamental processes: excitation, ionization, and few-electron dynamics in atoms and molecular bonding orbitals.(b): Impulsive phase control of resonant gain and absorption represents a disruptive key technology rivalling the LASER especially in the hard-x-ray domain, where long-lived population inversion in dense media seems impossible. Frequency combs around a well-defined (5 neV) hard-x-ray Mössbauer Fe57 nuclear transition (14.4 keV) will be demonstrated. Such combs (at >10 keV), will in the future allow the most sensitive tests of fundamental physics, e.g. quantum-electrodynamics (QED) in highly-charged ions and the variation of physical 'constants'."