Kernel functions play a pivotal role in the performance of Support Vector Machines (SVMs), particularly in handling non-linear datasets. This study explores and compares the efficacy of various SVM kernel functions—linear, radial basis function (RBF), polynomial, and sigmoid—alongside their combinations for classifying 2D non-linear datasets. Using the synthetic Moon and Circle datasets from scikit-learn as benchmarks, we evaluate the performance of these kernels based on classification accuracy, computational efficiency, and decision boundary characteristics. Additionally, we experiment with hybrid kernel approaches, aiming to leverage the strengths of individual kernels for improved performance. Recent advancements in multi-kernel learning and adaptive kernel selection are highlighted to contextualize the research. Results highlight the distinct advantages and limitations of each kernel type, offering insights into optimal kernel selection and combination strategies for non-linear datasets. This work provides a comprehensive understanding of SVM kernel behaviors, contributing to the broader field of machine learning model selection and kernel design, and offering practical guidelines for real-world applications.