Brain-computer interface (BCI) is an emerging communication technology that facilitates interaction between humans and external devices based on the user's thoughts. Motor imagery (MI) classification, using electroencephalography (EEG) to detect user's movement intentions, is a primary BCI research area. Mental arithmetic (MA) classification is also employed in the analysis of brain activity related to concentration and working memory in simple arithmetic operations such as addition and subtraction. In addition, recent advancements in data analysis techniques have enabled the active use of deep learning-based artificial intelligence models to analyze EEG signals. Accordingly in this thesis, a method for analyzing brain activity during MI and MA using a deep learning model based on EEG signals is proposed.This thesis is composed of contents related to MI and MA classification. In MI classification, a method of filtering out data that is considered to indicate a decrease in user's concentration was proposed, and it was confirmed that this led to an improvement in the model's classification performance. In the case of the data excluded from the training, there was a tendency for the motor-related potentials to not be observed. In MA classification, a graph neural network (GNN) model was proposed that achieves high classification performance using spatial brain activity and functional connectivity, and the explanation of the trained model operation based on explainable artificial intelligence was examined. The GNN utilized connectivity between the left centroparietal-left frontal regions and the frontoparietal connection as an important feature for mental arithmetic classification. The findings of this thesis are expected to provide valuable insights to future researchers who aim to advance brain-computer interface technology based on a thorough investigation of brain activity.