QSpace is an open-source tensor library designed to exploit quantum symmetry spaces in tensor network states for quantum many-body systems. It supports both Abelian and non-Abelian symmetries, including $\mathbb{Z}_n$, $U(1)$, and Lie algebras such as $A_n$, $B_n$, $C_n$, $D_n$, $\text{SU}(n)$, $\text{SO}(2n+1)$, $\text{Sp}(2n)$, and $\text{SO}(2n)$. The library is implemented in C++ and integrated into Matlab via MEX interfaces. QSpace's approach is bottom-up, starting from the defining representation and Lie algebra, and explicitly computing generalized Clebsch-Gordan coefficients (CGTs) to perform various operations across all symmetries. This allows for the development of tensor network algorithms that can fully exploit non-Abelian symmetries without explicit use of 6j-symbols, which are only analytically known for SU(2). The documentation covers the general approach and conventions of QSpace, including tensor storage, composite indices for state spaces, leg directions, pictorial representations, tensor conjugation, 1j symbols, and the handling of dual state spaces. It also provides detailed examples and tutorials for using QSpace in practical applications, such as building rank-5 PEPS tensors and iterative diagonalization of Wilson chains in the context of the finite density matrix renormalization group (fdm-NRG) and numerical renormalization group (NRG) methods. QSpace has a long history, starting from version 1 in 2006, which initially supported U(1) symmetries. Version 2 introduced non-Abelian symmetries, and version 3 completed the implementation of semi-simple symmetries. Version 4, released in 2022, is the first open-source version available on Bitbucket under the Apache 2.0 license. The documentation emphasizes the importance of symmetry in numerical simulations for both efficiency and physical insights, and provides comprehensive guidance for users familiar with tensor network states and quantum many-body systems.QSpace is an open-source tensor library designed to exploit quantum symmetry spaces in tensor network states for quantum many-body systems. It supports both Abelian and non-Abelian symmetries, including $\mathbb{Z}_n$, $U(1)$, and Lie algebras such as $A_n$, $B_n$, $C_n$, $D_n$, $\text{SU}(n)$, $\text{SO}(2n+1)$, $\text{Sp}(2n)$, and $\text{SO}(2n)$. The library is implemented in C++ and integrated into Matlab via MEX interfaces. QSpace's approach is bottom-up, starting from the defining representation and Lie algebra, and explicitly computing generalized Clebsch-Gordan coefficients (CGTs) to perform various operations across all symmetries. This allows for the development of tensor network algorithms that can fully exploit non-Abelian symmetries without explicit use of 6j-symbols, which are only analytically known for SU(2). The documentation covers the general approach and conventions of QSpace, including tensor storage, composite indices for state spaces, leg directions, pictorial representations, tensor conjugation, 1j symbols, and the handling of dual state spaces. It also provides detailed examples and tutorials for using QSpace in practical applications, such as building rank-5 PEPS tensors and iterative diagonalization of Wilson chains in the context of the finite density matrix renormalization group (fdm-NRG) and numerical renormalization group (NRG) methods. QSpace has a long history, starting from version 1 in 2006, which initially supported U(1) symmetries. Version 2 introduced non-Abelian symmetries, and version 3 completed the implementation of semi-simple symmetries. Version 4, released in 2022, is the first open-source version available on Bitbucket under the Apache 2.0 license. The documentation emphasizes the importance of symmetry in numerical simulations for both efficiency and physical insights, and provides comprehensive guidance for users familiar with tensor network states and quantum many-body systems.