In this Doctoral Thesis, we have examined the magnetoencephalography (MEG) background activity in 36 Alzheimer's disease (AD) patients and 26 elderly control subjects by means of non-linear methods. Our goal was to test the hypothesis that brain activity recorded in MEG signals is different in AD patients than in control subjects. AD is the most frequent form of dementia in western countries. This brain disorder affects 1% of the population aged 60-64 years, but the prevalence increases exponentially with age, so around 30% of people over 85 years suffer from this disease. Additionally, due to the fact that life expectancy has increased significantly in western countries during the last decades, it is expected that the number of people with dementia will increase to 81 million in 2040. As a definitive diagnosis is only possible by necropsy, the differential diagnosis with other types of dementia and with major depression is becoming more important. This differential diagnosis includes medical history, physical and neurological evaluation, laboratory studies and neuroimaging techniques. Mental status tests are also used to assess the severity of cognitive deficit. Diagnostic tools and criteria make possible for physicians to pursue a positive clinical diagnosis with an accuracy between 80 and 90%. Hence, new approaches are needed to improve AD detection. Nowadays, MEG recordings are not used in AD clinical diagnosis. Nevertheless, several studies have demonstrated that the analysis of brain signals could help physicians in the diagnosis of this dementia. MEG, as electroencephalography (EEG), is a non-invasive technique that allows to record the electromagnetic fields produced by brain activity with good temporal resolution. The vi use of MEG recordings to study the background brain activity offers some advantages over EEG. MEG provides reference-free recordings, which are not distorted by the resistive properties of the skull. Additionally, MEG offers higher spatial resolution than conventional EEG. On the other hand, the magnetic signals generated by the human brain are extremely weak. Thus, superconductive devices are necessary to detect them and MEGs must be recorded in a magnetically shielded room. Therefore, MEG is characterized by limited availability and high equipment cost. Non-linearity is present in many physiological signals. For a neuronal network such as the brain, non-linearity is introduced even at the cellular level, since the dynamical behaviour of individual neurons is governed by threshold and saturation phenomena. Moreover, non-linear methods have demonstrated their usefulness for the analysis of brain recordings in AD. For these reasons, we have examined the MEG background activity in AD patients and control subjects with several non-linear techniques: Lempel-Ziv complexity, Higuchi's fractal dimension, Maragos and Sun's fractal dimension, Shannon spectral entropy, approximate entropy, sample entropy, multiscale entropy, non-linear forecasting, auto mutual information, detrended fluctuation an...