In this section we will discuss the basic ideas behind coupled-cluster theory, including the cluster expansion, cluster operators, and size-extensivity. Throughout these notes, we will use the convention that one-electron states, i.e. spin orbitals, which are occupied (unoccupied) in the single reference wavefunction are denoted by i,j,k,l,...(a,b,c,d,...). General one-electron states will be denoted by p,q,r,s,....