This paper presents a fault-tolerant one-way quantum computer based on three-dimensional cluster states. The scheme uses topological error correction methods, linking cluster states to surface codes. The error threshold is 1.4% for local depolarizing errors and 0.11% for each source in an error model with preparation-, gate-, storage- and measurement errors. The quantum computation is performed on a three-dimensional cluster state via a sequence of one-qubit measurements. The cluster lattice is divided into three regions: V (vacuum), D (defect), and S (singular qubits). The S-qubits are measured in an adaptive basis and perform the non-Clifford part of the computation. The V and D regions are used to distribute quantum correlations among the S-qubits. The defects are topologically entangled and help guide quantum correlations. The paper describes the use of the planar code and the concatenated Reed-Muller code for error correction. The planar code has a high error threshold of about 11% and is well-suited for cluster states. The Reed-Muller code is used for fault-tolerant measurement of encoded observables. The paper also discusses the use of homology to characterize quantum correlations and errors. The error correction methods are based on the topological properties of the cluster state and the defects. The fault-tolerant quantum computation is achieved by using the Reed-Muller code to perform local measurements of encoded observables. The paper concludes with an overview of the error models, fault-tolerance threshold, and overhead of the scheme.This paper presents a fault-tolerant one-way quantum computer based on three-dimensional cluster states. The scheme uses topological error correction methods, linking cluster states to surface codes. The error threshold is 1.4% for local depolarizing errors and 0.11% for each source in an error model with preparation-, gate-, storage- and measurement errors. The quantum computation is performed on a three-dimensional cluster state via a sequence of one-qubit measurements. The cluster lattice is divided into three regions: V (vacuum), D (defect), and S (singular qubits). The S-qubits are measured in an adaptive basis and perform the non-Clifford part of the computation. The V and D regions are used to distribute quantum correlations among the S-qubits. The defects are topologically entangled and help guide quantum correlations. The paper describes the use of the planar code and the concatenated Reed-Muller code for error correction. The planar code has a high error threshold of about 11% and is well-suited for cluster states. The Reed-Muller code is used for fault-tolerant measurement of encoded observables. The paper also discusses the use of homology to characterize quantum correlations and errors. The error correction methods are based on the topological properties of the cluster state and the defects. The fault-tolerant quantum computation is achieved by using the Reed-Muller code to perform local measurements of encoded observables. The paper concludes with an overview of the error models, fault-tolerance threshold, and overhead of the scheme.