In this talk, we will discuss eigenvalues of tensors using Algebraic Geometry. We will define multiplicities of eigenvalues of tensors, which are generalizations of multiplicities of eigenvalues of matrices. It is well known that the geometric multiplicity of an eigenvalue of a matrix is no more than its the algebraic multiplicity. We will discuss a similar relation for tensors. If time permits, we will also discuss the inverse eigenvalue problem for tensors. We will show that the behavior of eigenvalues of tensors is very different from that of matrices. This is a joint work with Shenglong Hu.