In this thesis, we investigate the use of hierarchical low-rank approximations to mitigate the computational challenges associated with kernel matrix inversion. In particular, we focus on the Geometry-Oblivious Fast Multipole Method(GOFMM), which decomposes dense SPD kernel matrices into smaller, manageable low-rank blocks. This decomposition reduces the overall complexity of the inversion process to approximately O(N logN), while maintaining a high degree of accuracy. The GOFMM approach allows for scalable matrix inversion, making it feasible to apply kernel-based to significantly larger datasets. Wedevelop and implement algorithms based on GOFMM, optimizing them for parallel execution on multi-core system. Strong and weak scaling experiments are conducted to evaluate the performance of these algorithms across various setups. We test the methods on synthetic data and real-world datasets such as MNIST. The work presented in this document demonstrates that hierarchical low-rank approximations, specifically GOFMM,offerascalable andefficient alternative to traditional kernel matrix inversion techniques.