We present an integrative formalism of mutual information expansion, the general Poisson exact breakdown, which explicitly evaluates the informational contribution of correlations in the spike counts both between and within neurons. The formalism was validated on simulated data and applied to real neurons recorded from the rat somatosensory cortex. From the general Poisson exact breakdown, a considerable number of mutual information measures introduced in the neural computation literature can be directly derived, including the exact breakdown (Pola, Thiele, Hoffmann, & Panzeri, 2003), the Poisson exact breakdown (Scaglione, Foffani, Scannella, Cerutti, & Moxon, 2008) the synergy and redundancy between neurons (Schneidman, Bialek, & Berry, 2003), and the information lost by an optimal decoder that assumes the absence of correlations between neurons (Nirenberg & Latham, 2003; Pola et al., 2003). The general Poisson exact breakdown thus offers a convenient set of building blocks for studying the role of correlations in population codes.