These talks be a brief introduction to the Cauchy problem in Einstein's theory of general relativity. We will examine the Einstein field equations and focus on the role of initial data in the development of local and global results for space-times. Topics will include the constraint equations; the local existence results of Choquet-Bruhat and Choquet-Bruhat-Geroch; global hyperbolicity and the topology of space-time; asymptotically flat initial data sets and space-times; and trapped surfaces and marginally outer trapped surfaces (MOTS). The final talk will present recent results (in collaboration with Galloway and Eichmair) on singularity theorems and topological censorship from the initial data point of view.