In this talk, I will explain how Riemann-Roch spaces are defined. First, we will introduce the notions of valuations, places and divisors. Computing a basis of this space can be useful in error correction codes theory. We can also come across those spaces in cryptosystems based on a curve, where only one element of a Riemman-Roch space is needed to add two elements on the Jacobian of a curve. Then, I will present a method to compute a basis of a Riemann-Roch space on a function field. This amounts to reduce a basis of a certain fractional ideal.