An evolutionary process is frequently modeled as a sequence of the four bases A,C,G,T, each of them changing independently following a Markov process. The main goal of this project are two: first of all, we wanted to understand and explain, from a mathematically rigorous point of view, the modeling of an evolutionary process as a continuous Markov process, and why Lie Markov models are an adequate option for this task. Secondly, we explain how we tried to improve a previous implementation of Lie Markov models in IQ-TREE, an algorithm for inferring phylogenies.