MME – Mobility Management Entity.
The MME is responsible for initiating paging and authentication of the mobile device. MME retains location information at the tracking area level for each user and then selects the appropriate gateway during the initial registration process.
The S-GW is responsible for keeping track of devices when they move between eNobeB’s. This is typically not an extra piece of hardware just a function of the EPC
This is what connects the LTE network to the Capital I Internet. This also is typically not an extra piece of hardware just a function of the EPC
The S1 interface is described in the 3GPP TS 36.410 specification.
The X2 interface provides connectivity between two or more eNodeBs.