Electroencephalography (EEG) feature extraction plays a fundamental role in translating raw neural signals into meaningful representations for applications such as neurological diagnostics, brain-computer interfaces (BCIs), and cognitive state monitoring. This study presents a comprehensive comparative analysis of mathematical approaches employed in EEG feature extraction, categorized into time, frequency, time-frequency and nonlinear domains. In addition to reviewing existing methods, an experimental study was conducted using real EEG data from the Bonn University dataset. Features including statistical descriptors, Hjorth parameters, band powers, spectral entropy, approximate entropy, fractal dimension, Hurst exponent, and Lempel-Ziv complexity were systematically extracted and compared between healthy and seizure recordings. Furthermore, timefrequency representations were generated using Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) to capture transient and non-stationary dynamics. The results demonstrate that a multi-domain feature extraction strategy significantly enhances the ability to characterize and discriminate pathological EEG signals. Key challenges such as data variability, limited dataset availability, and the need for standardized analysis pipelines are also discussed, along with future directions including the development of benchmark datasets, explainable AI-driven feature selection, and real-time EEG processing optimization. By integrating theoretical insights with experimental validation, this study aims to support the development of more reliable, interpretable, and scalable EEG-based systems for scientific and clinical use.