This course is about the key numerical algorithms that you should really want to know about. How do GPS and TrueType fonts work? How to move a robot around? 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 least squares, Bézier curves, quadrature, 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, direct and iterative methods for solving linear systems of equations, and polynomial interpolation. 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.