This paper introduces a universal measure of quantum entanglement in the ground state of a topologically ordered two-dimensional system with a mass gap. The measure is called the topological entanglement entropy, denoted by $ -\gamma $, which is a universal constant characterizing the global properties of the entanglement. The entanglement entropy $ S(\rho) $ of a disk with boundary length $ L $ in the ground state has the form $ S(\rho) = \alpha L - \gamma + \cdots $, where $ \alpha $ is nonuniversal and ultraviolet divergent, while $ -\gamma $ is universal. The value of $ \gamma $ is derived using topological quantum field theory methods and is related to the quantum dimensions of the superselection sectors of the system. The topological entanglement entropy $ -\gamma $ is shown to be a topological invariant, dependent only on the topology of the system and not on its geometry. It is calculated using a combination of entropies of different regions of the system, which ensures that the dependence on the boundary length cancels out. The result is $ S_{topo} = -\gamma $, where $ \gamma = \log \mathcal{D} $, and $ \mathcal{D} $ is the total quantum dimension of the system, given by $ \mathcal{D} = \sqrt{\sum_{a} d_{a}^{2}} $, with $ d_{a} $ being the quantum dimension of each superselection sector. The paper also discusses the implications of this result for different types of topological order, including abelian and non-abelian anyons. It shows that the topological entanglement entropy can be used to characterize the topological order of a system and is invariant under smooth deformations of the Hamiltonian unless a quantum critical point is encountered. The results are supported by a variety of examples, including the Laughlin state and the toric code. The paper concludes with a discussion of the broader implications of the results for understanding topological order and the construction of explicit microscopic models that realize it.This paper introduces a universal measure of quantum entanglement in the ground state of a topologically ordered two-dimensional system with a mass gap. The measure is called the topological entanglement entropy, denoted by $ -\gamma $, which is a universal constant characterizing the global properties of the entanglement. The entanglement entropy $ S(\rho) $ of a disk with boundary length $ L $ in the ground state has the form $ S(\rho) = \alpha L - \gamma + \cdots $, where $ \alpha $ is nonuniversal and ultraviolet divergent, while $ -\gamma $ is universal. The value of $ \gamma $ is derived using topological quantum field theory methods and is related to the quantum dimensions of the superselection sectors of the system. The topological entanglement entropy $ -\gamma $ is shown to be a topological invariant, dependent only on the topology of the system and not on its geometry. It is calculated using a combination of entropies of different regions of the system, which ensures that the dependence on the boundary length cancels out. The result is $ S_{topo} = -\gamma $, where $ \gamma = \log \mathcal{D} $, and $ \mathcal{D} $ is the total quantum dimension of the system, given by $ \mathcal{D} = \sqrt{\sum_{a} d_{a}^{2}} $, with $ d_{a} $ being the quantum dimension of each superselection sector. The paper also discusses the implications of this result for different types of topological order, including abelian and non-abelian anyons. It shows that the topological entanglement entropy can be used to characterize the topological order of a system and is invariant under smooth deformations of the Hamiltonian unless a quantum critical point is encountered. The results are supported by a variety of examples, including the Laughlin state and the toric code. The paper concludes with a discussion of the broader implications of the results for understanding topological order and the construction of explicit microscopic models that realize it.