This thesis considers solutions to the discrete Nagumo equation u˙ n = d(un−1 − 2un + un+1) + f(un), n ∈ Z. For sufficiently large d, the solutions are of the form un(t) = U(n + ct) with c > 0. This thesis contains the proof of existence of traveling wave solutions of the discrete Nagumo equations and originates from Bertram Zinner’s article ”Existence of Traveling Wavefront Solutions for the Discrete Nagumo equation” [Zin90]. In the first chapter, all the prerequisite knowledge needed to understand the proof, such as Brouwer’s fixed point theorem, is presented. The proof starts by considering f(un) as a linear function and thus simplifying the problem. The simplified problem is converted into a fixed point problem by considering a Poincar´e map which can be solved using Brouwer’s fixed point theorem. Finally, the proof ends by confirming that the solutions of the approximated, simplified problem have a limit point which corresponds to the traveling wave solutions of the discrete Nagumo equation