Epilepsy is one of the most common neurological disorders that can be diagnosed through electroencephalogram (EEG), in which the following epileptic events can be observed: pre-ictal, ictal, post-ictal, and interictal. In this paper, we present a novel method for epilepsy detection into two differentiation contexts: binary and multiclass classification. For feature extraction, a total of 105 measures were extracted from power spectrum, spectrogram, and bispectrogram. For classifier building, eight different machine learning algorithms were used. Our method was applied in a widely used EEG database. As a result, random forest and backpropagation based on multilayer perceptron algorithms reached the highest accuracy for binary (98.75%) and multiclass (96.25%) classification problems, respectively. Subsequently, the statistical tests did not find a model that would achieve a better performance than the other classifiers. In the evaluation based on confusion matrices, it was also not possible to identify a classifier that stands out in relation to other models for EEG classification. Even so, our results are promising and competitive with the findings in the literature.