Catalan and catalan like triangles

This thesis consists of four main sections. In the first section, a literature review is given on Catalan and Hosoya triangles. In addition, some basic information is given on binomial coefficients, combination properties and Pascal triangle. In the second section; central binomial coefficients and their relationship with Catalan numbers are mentioned. Some important properties such as Catalan numbers, generating function for Catalan numbers and approximate value of Catalan numbers are also mentioned. Finally, in the third and fourth sections of the thesis, Catalan triangle and Hosoya triangle, which have a similar structure to Pascal triangle, are mentioned. Catalan triangle of Pascal triangle and some important properties are given.