Epilepsy is a neurological disorder that is characterized by recurring seizures. Seizures are electrical disturbances in the brain that develop suddenly and uncontrollably. They can cause various symptoms, depending on what part of the brain is affected. The cause of epilepsy is often unknown, but it can be caused by brain injury, brain infections, genetics, or other medical conditions. EEG analysis is a very important aspect of the diagnosis and treatment of epilepsy. It includes the interpretation of electrical activity patterns recorded from the electrodes. In this study, the machine learning methods and deep learning methods have been examined for epilepsy diagnosis. Random Forest (RF), Naive Bayes (NB) algorithm, Support Vector Machine (SVM), Levenberg-Marguardt (LM), and Long Short Term Memory (LSTM) were used for classification, while the Welch method has been used for feature extraction. The Bonn EEG dataset has been used for application. As a result, the RF method showed the best accuracy as 99.87%. RF achieved 99.84% precision, 99.9% sensitivity, 99.87% F1-Score, and 99.87 AUC. LSTM achieved the second accuracy degree as 99.39%.