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Analytic theory for strongly-coupled microring resonators of general 2-D coupling topologies is developed based on the field coupling formalism. The theory allows simple characteristic equation for coupled microring resonators (CMR) of general coupling topology to be formulated, from which closed form analytical expressions of the transmission responses of the device can be derived. It is also shown that any CMR structure is characterized by a field coupling matrix which can be decomposed into a direct and indirect coupling term. The indirect coupling matrix can give rise to prominent strong coupling effects, such as indirect coupling induced transparency, that are not observed in weakly coupled microring resonators.