This chapter investigates data-dependent generalization error bounds, which enable estimating model performance directly from training data. Central to this analysis is the interplay between Rademacher complexity and VC dimension, two complementary measures of model capacity. While VC dimension provides a worst-case theoretical framework, the chapter emphasizes empirical Rademacher complexity–a data-driven metric that quantifies how well a function class can fit random noise. This empirical approach facilitates tighter generalization bounds compared to traditional VC-based methods. The discussion further explores regularization as a practical implementation of the Structural Risk Minimization (SRM) principle, where penalty terms constrain model complexity to mitigate overfitting. In multi-class classification, the chapter contrasts uncombined strategies (reducing the problem to binary tasks) with combined methods (solving a unified optimization problem via joint loss functions). Finally, it extends data-dependent generalization bounds to multi-class settings by adapting Rademacher complexity concepts, ensuring robust theoretical guarantees even for complex, high-dimensional learning scenarios. These insights collectively bridge theoretical rigor with practical algorithmic design, enhancing the understanding of model generalization across diverse learning tasks.