This paper introduces a canonical basis B for the positive part U⁺ of the quantized enveloping algebra associated with a root system. The basis is constructed using properties of PBW bases and representation theory of quivers. The canonical basis B is defined as a Z[v⁻¹]-basis of a submodule L of U⁺, which is invariant under certain automorphisms. It is shown that B is fixed by a specific involution on U⁺ and that its image under a natural projection is a Z-basis of L/v⁻¹L. The paper also explores the relationship between the canonical basis and the representation theory of quivers, showing that the dimension of orbits of representations can be computed explicitly. The canonical basis has remarkable properties, including the fact that the product of two elements in B is a linear combination of elements in B with coefficients in Z[v, v⁻¹]. The paper also discusses the relationship between the canonical basis and finite-dimensional modules of U, showing that the basis provides a canonical basis for these modules. The paper concludes with a discussion of the cyclic quiver and the non-simply laced case.This paper introduces a canonical basis B for the positive part U⁺ of the quantized enveloping algebra associated with a root system. The basis is constructed using properties of PBW bases and representation theory of quivers. The canonical basis B is defined as a Z[v⁻¹]-basis of a submodule L of U⁺, which is invariant under certain automorphisms. It is shown that B is fixed by a specific involution on U⁺ and that its image under a natural projection is a Z-basis of L/v⁻¹L. The paper also explores the relationship between the canonical basis and the representation theory of quivers, showing that the dimension of orbits of representations can be computed explicitly. The canonical basis has remarkable properties, including the fact that the product of two elements in B is a linear combination of elements in B with coefficients in Z[v, v⁻¹]. The paper also discusses the relationship between the canonical basis and finite-dimensional modules of U, showing that the basis provides a canonical basis for these modules. The paper concludes with a discussion of the cyclic quiver and the non-simply laced case.