New mental tasks were investigated for suitability in Brain-Computer Interface (BCI). Electroencephalography (EEG) signals were collected and analyzed to identify these mental tasks. MS Windows-based software was developed for investigating and classifying recorded EEG data with unnecessary frequencies filtered out with Bandpass filtering. To identify the best feature vector construction method for a given mental task, feature vectors were constructed using Bandpower, Principal Component Analysis, and Downsampling separately. These feature vectors were then classified with Linear Discriminant Analysis, Linear Support Vector Machines, Critical Distance Classifiers, Nearest Neighbor Classifiers, and their Non-Linear counterparts to find the best-performing classifier. For comparison purposes, performances of already well-known mental tasks in the BCI community were computed along with that of new mental tasks introduced in this thesis. In the preliminary studies, it was found that the most promising new mental task which a BCI system could identify is the imagination of hitting a given square with an imaginary arrow from above (or below) and right, (or left) to the screen. The group of these mental tasks was named as 'Hit Series' (HS). A detailed investigation of HS was carried out and compared with the performance of Motor Imagery (MI) events which are the most heavily used mental tasks in EEG-based BCI systems. One subject achieved the maximum average performance for HS, 100 pct in the binary classifications while 99 pct in overall combined performance. The best average performances of the other two subjects for the same mental tasks were 93 pct and 87pct with the overall performance of 89 pct and 78 pct. Performances of the same three subjects for mental tasks in MI were relatively poor. The average performances were 92, 78, and 92 pct while overall performances were 87, 69, and 88 pct.