For any permutation \(w=w_1w_2\ldots w_n\in S_n\), we call a positive integer \(i\) a descent if \(w_i>w_{i+1}\). Eulerian number denoted \(\genfrac{<}{>}{0pt}{}{n}{k}\) is the number of permutations in \(S_n\) with exactly \(k\) descents. Denoting by \(S_n(231)\) the set of permutations in \(S_n\) not containing the pattern 231, Narayana number \(N_{n,k}\) is the number of permutations in \(S_n(231)\) with \(k\) descents. This Master’s thesis consists of three chapters. The first chapter contains some introductory notions and results needed in the rest of the work. The second chapter examines Eulerian numbers starting from their definition and basic properties. We introduce the Eulerian polynomials and prove two important identities finishing this part with a problem from geometry where Eulerian numbers make an unexpected appearance. The third chapter treats the Narayana numbers which are closely connected to Eulerian numbers. Catalan numbers also play an important role in this chapter since Narayana numbers are shown to be their refinement. Several examples where Narayana numbers appear are presented and their generating function is obtained.