Dive into the world of parameterized complexity with this introductory lecture on parameterized algorithms. Explore fundamental techniques for designing efficient algorithms, including branching, color coding, kernelization, and width-based dynamic programming. Progress to more advanced topics in discrete optimization, such as LP-guided branching and kernelization, Lenstra's algorithm for integer linear programming in fixed dimension, and methods for solving structured ILPs using Graver bases. Gain a solid foundation in this important area of computer science and mathematics through clear explanations and examples provided by Michal Pilipczuk from the Hausdorff Center for Mathematics.