The chapter contains modern group-theoretical approach to the wavefunction of a Cooper pair, developed in recent years. Two-electron states in solids obeying Pauli exclusion principle are considered making use of MackeyMackey theorem on symmetrized squaresSymmetrized square of induced representations. Such a state with zero total momentum corresponds to Cooper pairs in crystal solids. This approach, also called a space-group approach to the wavefunction of a Cooper pair, is applied to the groups \(D_{2h}\) , \(D_{4h}\) and \(D_{6h}\) , and \(T_{h}\) , i.e. symmetry groups of topological superconductors UTe \(_{2}\) , Sr \(_{2}\) RuO \(_{4}\) , UPt \(_{3}\) and PrOs \(_{4}\) Sb \(_{12}\) and possible pairs’ symmetries in symmetry points, directions and planes in BZs are considered. Special attention is given for non-symmorphic groups, coupling with nonzero angular momentum and time-reversal symmetry. Additional quantum numbers for Cooper pairs belonging to two-dimensional IRs are introduced. The group theoretical approach is further developed to incorporate phase winding and the applications are considered.