Abstract: In this talk, we provide universal constructions of irreducible representations of Leavitt path algebras via infinite irrational paths and pairs (c, f) consisting of simple closed paths c together with irreducible polynomials f in K[x]. Also, we give a new class of automorphisms of Leavitt path algebras. Consequently, we obtain Anick type automorphisms of Leavitt path algebras and new irreducible representations of Leavitt algebras of type (1, n). This is joint work with Prof. Phạm Ngọc Ánh and Prof. Shigeru Kuroda.