Preserving the information during its processing is of fundamental importance, and this is the main focus of quantum error correction. On the one hand, we should face the problem of errors during the transmission and the storing of quantum information. Here, we show how the three-qubit code (the Shor code) can take care of this issue in the presence of the main errors affecting the qubits (bit flip, phase flip and bit-phase flip). On the other hand, we must avoid the propagation and the accumulation of error due to faulty gates. To this aim, we explain the basic aspects of the fault-tolerant quantum computation and one of its most relevant results: the threshold theorem for quantum computation.