Tabular data analysis presents unique challenges due to its heterogeneous feature types, missing values, and complex interactions. While traditional machine learning methods, such as gradient boosting, often outperform deep learning approaches, recent advancements in neural architectures offer promising alternatives. This paper introduces TabKAN, a novel framework that advances tabular data modeling using Kolmogorov-Arnold Networks (KANs). Unlike conventional deep learning models, KANs leverage learnable activation functions on edges, enhancing both interpretability and training efficiency. Our contributions include: (1) the introduction of modular KAN-based architectures tailored for tabular data analysis, (2) the development of a transfer learning framework for KAN models, enabling effective knowledge transfer between domains, (3) the development of model-specific interpretability for tabular data learning, reducing reliance on post hoc and model-agnostic analysis, and (4) comprehensive evaluation of vanilla supervised learning across binary and multi-class classification tasks. Through extensive benchmarking on diverse public datasets, TabKAN demonstrates superior performance in supervised learning while significantly outperforming classical and Transformer-based models in transfer learning scenarios. Our findings highlight the advantage of KAN-based architectures in efficiently transferring knowledge across domains, bridging the gap between traditional machine learning and deep learning for structured data.