The goal of electronic structure theory is to solve the time-independent Schrodinger equation with a method that scales polynomially with the system size. The problem has been solved in the weakly-correlated regime, where coupled cluster theory (CC) with singles, doubles and perturbative triples (CCSD(T)) can achieve chemical accuracy. However, in the strongly-correlated regime, where the two-body interaction dominates, there are still no methods that can achieve a comparable accomplishment.

Strong correlation always comes hand in hand with spontaneous symmetry breaking in mean-field theory. For example, coupled cluster theory faces a symmetry dilemma in the strongly correlated regime, where it either completely fails to describe the system if symmetry adapted, or has to artificially break certain symmetries in order to produce reasonable energies. It is plausible that the problem of strong correlation can be solved by curing the symptoms, i.e., fixing the symmetries.

Symmetry projection has been carried out at the mean-field level, but it was unclear until this work how to incorporate correlation on top of it because of the language barrier between symmetry projection and coupled cluster theory. This thesis is devoted to combining CC and symmetry projection, focusing on spin and number symmetry. Different flavours of theories are obtained depending on whether a restricted or unrestricted reference is used. On the restricted side, the spin projected unrestricted Hartree Fock (SUHF) state can be rewritten as a polynomial of particle-hole excitations, acting on the restricted reference. Thus, this formalism opens up many ways to combine SUHF with CC. One the unrestricted side, the concept of disentangled cluster is introduced to describe the CC wavefunction transformed by symmetry rotation. A scheme basing on differential equations is devised to approximate these disentangled clusters, which scales polynomially and is systematically improvable. By combining symmetry projection and coupled cluster theory, the symmetry dilemma can be solved to a good extent.