The project introduces a new paradigm, the molecular spin quantum processor, in the world of quantum technologies. Artificial magnetic molecules that realize spin qudits, with multiple addressable quantum spin states, are controlled, read-out and linked via their coherent coupling to on-chip superconducting circuits. This scheme integrates quantum functionalities at three different scales (nuclear spins, electronic spins and circuits), is inherently modular and therefore scalable, and is also very flexible. It admits different qudit realizations, can create diverse qubit arrays and topologies and perform quantum simulations and fault-tolerant quantum computing, with quantum error correction either embedded in each molecule or distributed among different nodes in a topological lattice. FATMOLS objective is to provide a proof-of-concept of one of the repetition unit cells of this platform, involving at least two molecules with multiple and fully addressable levels, from which more complex architectures can be created. To achieve this goal, FATMOLS will design suitable algorithms and architectures for specific applications (quantum chemistry simulations, quantum error correction) and create, test and interconnect the different components (molecules, superconducting nano-resonators and control electronics) of this technology through a creative collaboration between disciplines and between top-level academic and industrial partners. In the short term, the project will reshape multi-frequency magnetic resonance instrumentation, a key enabling technology of widespread use. In the medium to long term, it will define an alternative roadmap to reach the next level of computational power (100-1000 qubits) and therefore address quantum optimization and quantum simulation problems with direct impact on diverse economic sectors (agriculture, health-care, energy, AI,…).