We derive four distinct identities for Green's functions, based on the generalized second theorem of Green. One of them is the generalized first theorem of Green, which can be used to derive the source-receiver reciprocity relation for Green's functions. Two identities give the sum or difference of the Green's function between two locations A and B as an integral sum of cross-convolutions of Green's functions from sources throughout the volume and/or over the surface, and received in A and B. Two other identities give the sum or difference of the Green's function and its time-reversed version between two locations A and B as an integral sum of cross-correlations of Green's functions from sources throughout the volume and/or over the surface, and received in A and B.