Computer Algebra, or Symbolic Computation, consists of representing and manipulating mathematical objects on a computer in an exact way, in contrast with the traditional scientific computing. In this course, we present a very active research topic in Computer Algebra – the development of algorithms for symbolic summation and symbolic integration. The emergence of these algorithms has put an important family of computational tools in the hands of discrete mathematicians, and many results that were inaccessible in other ways have been found and proved by computer methods. These algorithms are also nowadays unavoidable in physics, for the numerical evaluation of special functions, and more broadly for the difficult questions of simplification of formulas.