The physics of condensed matter depends on ultrafast dynamics of its atomic constituents. Femtosecond light pulses have been exploited to monitor these phenomena by stroboscopic means. Yet, the time resolution is limited by the duration of the intensity envelope of the light pulses used. We propose a new class of sub-cycle optics, which harnesses the absolute optical phase and amplitude of ultrashort transients to control condensed matter faster than an oscillation cycle of light. Merging latest terahertz technology with nanooptics, we tailor extreme electric and magnetic near-fields of phase-locked infrared pulses in all four spatio-temporal dimensions. This unprecedented laboratory allows us to pioneer long sought-after non-adiabatic quantum physics of all relevant elementary degrees of freedom: electronic charge and spin as well as photons.(i) Optical acceleration of electrons in the sub-cycle limit will permit to test yet unobserved key concepts of relativistic quantum transport, such as Zitterbewegung of Dirac fermions and Bloch oscillations in bulk semiconductors.(ii) We aim to switch the spin direction in magnetic materials by giant magnetic or electric fields, of 10 GV/m and several 10 Tesla, promising record control speeds and unique vistas onto the fastest magnetic elementary processes.(iii) By advancing the sensitivity of electro-optic sampling to the few-photon level the quantum nature of the oscillating carrier wave will be detected in the time domain. Spontaneous creation of photons out of quantum vacua, reminiscent of Hawking radiation of black holes, may be traced.The project breaks grounds for basic research, shedding new light onto the foundations of quantum electrodynamics, solid state physics and magnetism, as well as a new kind of field resolved quantum optics.