In this paper, we analyze the capacity region of a communication network where a Multiple Access Channel (MAC) and a point-to-point channel share a same medium and interfere with each other, where the transmitter of the point-to-point channel has cognitive capabilities. We introduce Multiple Access-Cognitive Interference Channel (MA-CIFC), with a two-user MAC as a primary network and a cognitive transmitter-receiver pair in which the cognitive transmitter knows the message being sent by all of the transmitters in a non-causal manner. We obtain an inner bound on the capacity region of MA-CIFC and derive two sets of strong interference conditions under which we establish the capacity regions. We also consider the Gaussian case and find capacity results for Gaussian MA-CIFC. Some numerical examples are also provided.