The effect of anesthesia on patient is expressed as the depth of anesthesia. The detection of appropriate depth of anesthesia is a matter of great importance in surgery. Too deep or too little anesthesia implementation may lead to many psychological and physical disorders on patients. Therefore it is necessary to keep the patient at the most appropriate level of anesthesia. This process is important and challenging operation. In this study, a system is proposed which can be used to determine the depth of anesthesia in order to assist physician. Anesthetic substances significantly affect the cortex of the brain. There are studies for determination of depth of anesthesia by monitoring of brain activity. In this study, EEG signals that reflect the brain activity are utilized to measure the depth of anesthesia. The study consists of feature extraction and classification stages of the EEG signal. In the feature extraction stage, a new attribute set consisting of 44 attributes in different categories was obtained. In this way, it is aimed to create an effective set of attributes that can represent EEG signals. The obtained attributes were used as input parameters for classification algorithms. In classification stage, the classification problem is classified by seven different classification algorithms. In this way, comparison of calculation time and accuracy for obtained results in different classification algorithms was provided. With the proposed method for the determination of different depth of anesthesia, 98.169% classification accuracy was achieved.