Human epilepsy is a disease characterized by sudden, unprovoked, recurrent seizures accompanied by pathological electrical activity in the brain, and is frequently resistant to drug treatment. The ability to anticipate the onset of these incapacitating episodes would -hopefully- permit clinical interventions and avoid the serious consequences they may provoque. In this work we first consider the problem of detection of the onset of an epileptic seizure, comparing linear and non-linear techniques of time series analysis applied to electro-encephalogram recordings against onset times determined clinically. Automatic detection would be useful for fast seizure recognition which is of importance for further diagnostic procedures. The second, more ambitious goal is to foresee the ocurrence of an upcoming seizure, exploiting the widely conjectured "decrease in complexity" associated with ictal episodes. Roughly speaking, we monitor changes in time-varying windowed estimates of different magnitudes characterizing the brain's intrinsic dynamics. We face these problems for five seizures belonging to a single patient, using two strategies of brain activity reconstruction: single and multiple-channel delay embedding of the dynamics. We have found that the studied approaches successfully reflect the non-stationary character of ictal episodes, and seizure onsets were clearly accussed. For prediction, the criteria employed in the determination of clinical onset times appeared crucial.