I will discuss the basics of a unitary and UV complete string theory described by a 2D QFT which in flat spacetime enjoys a (string-)Galilean invariant global symmetry. This type of string theory is referred to as nonrelativistic string theory. The spacetime geometry that this string theory couples to is non-Riemannian and is dubbed as the string Newton-Cartan geometry. I will derive the spacetime equations of motion by analyzing the worldsheet Weyl invariance at the quantum level. Finally, via a T-duality transformation, I will show how nonrelativistic string theory is related to the discrete light cone quantization (DLCQ) of relativistic string theory. The DLCQ of string/M-theory has played a central role in nonperturbative approaches, most notably in Matrix theory.