"It is important to prove, is more but it important to improve." This textbook is an introduction to Scientific Computing. We will illustrate several numerical methods for the computer solution of cer- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. With this aim, in Chapter 1 we will illustrate the rules of the game that computers adopt when storing and operating with real and complex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will adopt the programming environment MATLAB (R) 1 as a faithful companion. We will gradually discover its principal commands, statements and con- structs. We will show how to execute all the algorithms that we intro- duce throughout the book. This will enable us to furnish an immediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raised through exercises and examples, often stemming from specific ap- plications.