Many pioneering advances in medicine and biology require observation of the microscopic world with high resolution and without damaging the specimen. One of the most widespread techniques is multiphoton fluorescence microscopy, which allows full 3D imaging via optical sectioning, i.e., imaging of planes within the sample without the need for physical slicing. This technique has a major limitation, however: the penetration depth and the signal-to-noise ratio are not sufficient for imaging deep within tissue, preventing functional imaging of, e.g., neuronal or cardiac activity beyond superficial layers. QuNIm aims to transform the field of nonlinear imaging and microscopy by exploiting the unique properties of entanglement, a quantum mechanical superposition of two or more photons that behave like single particles. Two quantum-correlated photons are absorbed in a nonlinear process as a single particle, an event 10 billion times more probable than the absorption of two classical photons. QuNIm will apply, for the first time, the innovative concepts of spatiotemporal and multimode entanglement, super-Poissonian fluctuations, and macroscopic quantum beams to deliver a ground-breaking imaging technique. It will maintain the strengths of standard nonlinear imaging (e.g., multiphoton microscopy, boasting high resolution, 3D imaging and molecular specificity using fluorophores/photoproteins) while increasing its penetration depth and removing the drawbacks (complex ultrashort pulsed lasers, lengthy scanning procedures, and phototoxicity). QuNIm will further extend the limit of deep-tissue imaging while at the same time enhancing the contrast and reducing the laser intensity (mitigating tissue damage), delivering a transformative impact in different fields. For example, in neuroscience, this will allow imaging of, e.g. sub-cortical brain regions fundamental for important studies into learning, memory and degenerative neural conditions such as Alzheimer's disease.