Modeling complex phenomena across disciplines such as physics, engineering, and the biological sciences often relies on advanced numerical methods to achieve accurate representations of real-world systems. However, these approaches can be computationally demanding and time-intensive, particularly when large-scale simulations are involved. To address these challenges, efficient parallel algorithms have been developed that deliver results comparable to their serial counterparts while significantly reducing computational cost through parallel execution. Examples of such techniques include domain decomposition methods, parallel iterative and direct linear solvers, shared-memory and distributed-memory programming models, GPU acceleration, and mixed-precision algorithms. The course introduces the fundamental concepts of High-Performance Computing (HPC), including modern CPU and GPU architectures, performance analysis tools such as the roofline model, and strong/weak scaling metrics. Students will gain practical experience with parallel programming paradigms, including MPI, OpenMP, and GPU computing. The course also presents applications of scalable linear solvers and domain decomposition strategies in combination with numerical discretization methods such as Finite Volume and Galerkin methods.