In this paper, the following three methods are presented to construct triangular norms on partially ordered sets: (1) Constructing triangular norms on the poset of closed intervals. (2) Constructing triangular norms via Galois connections between bounded posets based on a categorical analysis of the construction of triangular norms on closed intervals via monotone functions and their pseudo inverses. (3) Constructing triangular norms on function spaces between partially ordered sets. Particularly, the method by Galois connections between partially ordered sets is a general and useful method. Properties and more construction methods of triangular norms on partially ordered sets, possibly with the theory of triangular norms on the unit interval as prototype, deserve further investigations.