Electroencephalography (EEG) signals are frequently used for the detection of epileptic seizures. In this chapter, advanced signal analysis methods such as Empirical Mode Decomposition (EMD), Ensembe (EMD), Dynamic mode decomposition (DMD), and Synchrosqueezing Transform (SST) are utilized to classify epileptic EEG signals. EMD and its derivative, EEMD are recently developed methods used to decompose nonstationary and nonlinear signals such as EEG into a finite number of oscillations called intrinsic mode functions (IMFs). In this study multichannel EEG signals collected from epilepsy patients are decomposed into IMFs, and then essential IMFs are selected. Finally, time-and spectral-domain, and nonlinear features are extracted from selected IMFs and classified. DMD is a new matrix decomposition method proposed as an iterative solution to problems in fluid flow analysis. We present single-channel, and multi-channel EEG based DMD approaches for the analysis of epileptic EEG signals. As a third method, we use the SST representations of seizure and pre-seizure EEG data. Various features are calculated and classified by Support Vector Machine (SVM), k-Nearest Neighbor (kNN), Naive Bayes (NB), Logistic Regression (LR), Boosted Trees (BT), and Subspace kNN (S-kNN) to detect pre-seizure and seizure signals. Simulation results demonstrate that the proposed approaches achieve outstanding validation accuracy rates.