This course is about the key numerical algorithms that you should really want to know about. How do TrueType fonts work? What is the secret of Google's success? Why is JPEG compression so efficient? The answers to these questions are clever numerical algorithms, based on Bézier curves, eigenvalues, and the discrete cosine transformation, respectively. We will be able to understand and discuss them once we have gone through some preliminary basics, including Newton's method for finding roots, polynomial interpolation, direct and iterative methods for solving linear systems of equations, and Gaussian quadrature. This course refreshes your basic math skills in calculus and linear algebra and shows how to utilize them for solving several real-world problems, like the ones mentioned earlier. We also provide references to the history of these solutions, going back to Newton, Leibniz, Euler, Gauss and others.