Quantum registers of nuclear spins coupled to electron spins of individual solid-state defects are a promising platform for quantum information processing [1][2][3][4][5][6][7][8][9][10][11][12][13]. Pioneering experiments selected defects with favourably located nuclear spins having particularly strong hyperfine couplings [4][5][6][7][8][9][10]. For progress towards large-scale applications, larger and deterministically available nuclear registers are highly desirable. Here we realize universal control over multi-qubit spin registers by harnessing abundant weakly coupled nuclear spins. We use the electron spin of a nitrogen-vacancy centre in diamond to selectively initialize, control and read out carbon-13 spins in the surrounding spin bath and construct high-fidelity single-and two-qubit gates. We exploit these new capabilities to implement a three-qubit quantum-error-correction protocol [14][15][16][17] and demonstrate the robustness of the encoded state against applied errors. These results transform weakly coupled nuclear spins from a source of decoherence into a reliable resource, paving the way towards extended quantum networks and surface-code quantum computing based on multi-qubit nodes [11,18,19].Electron and nuclear spins associated with defects in solids provide natural hybrid quantum registers [3][4][5][6][7][8][9][10][11]. Fullycontrolled registers of multiple spins hold great promise as building blocks for quantum networks [18] and fault-tolerant quantum computing [19]. The defect electron spin enables initialization and readout of the register and coupling to other (distant) electron spins [11,18], whereas the nuclear spins provide well-isolated qubits and memories with long coherence times [8,9,11]. Previous experiments relied on selected defects having nuclear spins with strong hyperfine couplings that exceed the inverse of the electron spin dephasing time (1/T * 2 ). With these strongly coupled spins, singleshot readout [9,10,[20][21][22] and entanglement [9,11] were demonstrated. However, the number of strongly coupled spins varies per defect and is intrinsically limited, so that universal control has so far been restricted to two-qubit registers [4,7] and the required control of multi-qubit registers has remained an open challenge.Here we overcome this challenge by demonstrating universal control of weakly coupled nuclear spins (unresolved hyperfine coupling 1/T * 2 ). We use the electron spin of single nitrogen-vacancy (NV) centres in room-temperature diamond to selectively control multiple carbon-13 ( 13 C) nuclear spins in the surrounding spin bath (Fig. 1a). With this new level of control we realize multi-qubit registers by constructing high-fidelity unconditional and electroncontrolled gates, implementing initialization and readout, and creating nuclear-nuclear entangling gates through the electron spin. Finally, we demonstrate the power of this approach by implementing the first quantum-error-correction protocol with individual solid-state spins.We have used dynamical decoupling spect...