Atrial fibrillation (AF) is one of the most common cardiac arrhythmias, affecting around 10% of the population older than 70 years. In spite of its high incidence in the population, the mechanisms that trigger and maintain AF are uncertain. Although diverse surgical and pharmacological treatments exist, their success is very low. The cause of this low rate of success of the different therapies is the lack of a patient selection criterium that allows to predict which therapy will be more effective for each patient. Measurement of atrial organization has been proposed as a marker of the degree of severity of the arrhythmia in each patient, and thus a potential predictor of the success of therapeutical strategies. This doctoral thesis is related to the noninvasive determination of the degree of spatial organization of the atrial activation from the study of multiple electrocardiographic recordings. The electrocardiogram (ECG) is a simplified representation of the electrical field of the heart based on its projection on 8 axis. This simplification is considered as acceptable in the case of non-fibrillating rhythms in which myocardial activation can be modelled as a dipole. However, its validity has not been demonstrated for the case of fibrillating rhythms in which the assumption of a dipolar model is questionable. One of the objectives of this thesis has been the evaluation of the suitability of the ECG for obtaining spatial characteristics of AF waves. Three-dimensional representations of AF waves obtained from three recorded orthogonal leads were compared to three-dimensional representations obtained from orthogonal leads estimated from the standard ECG. We concluded that estimated three-dimensional representations of AF loops are not accurate. The results of our study show that the lack of dipolarity of AF waves does not allow the estimation of spatial parameters from the standard ECG. In order to have an accurate representation of AF waves it is necessary, therefore, to have a greater number of electrocardiographic derivations that allow us to determinate the potentials on the entire surface of the torso during AF. An objective of this thesis has been the determination of the minimum number of derivations that are necessary to accurately estimate surface potentials during AF by analyzing of the statistics of the signal. This study has allowed us to determine that the degree of complexity of the electrical activation during AF forces the use of three times more electrodes to achieve similar accuracy than the standard ECG for the representation of the electrical activation during non-fibrillanting rhythms. Making use of the sufficient number of electrodes it is possible to represent the trajectory of AF waves in the space. This spatial representation has allowed us to observe different patterns of electrical activation such as the propagation of a single wavefront or the appearance of multiple simultaneous wavefronts. This is the first time these patterns, consistent with patterns obtained from invasive recordings, have been evaluated by making use of noninvasive recordings. Spatial representations of the electrical activation on the body surface during AF may provide a deeper knowledge of the degree of atrial organization during AF and can help, therefore, to select the most appropriate treatment for each patient.