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When data is provided in an unstructured format or is high-dimensional, classical interpolation or approximation schemes as Finite-Element Methods (FEM) struggle to be accurate and efficient. An alternative is provided by kernel-based approaches in the Reproducing Kernel Hilbert space (RKHS) framework. Common applications range from support vector machines in context of machine learning to reconstruction of image data. In this course, we will introduce the framework for kernel-based approximation schemes and discuss how one can implement them efficiently. At the end we will look at possible applications of kernel-based methods in context of fluid dynamics and particle methods.