Graduate Program in Physics.Bleeken, Dieter Van den.Aras, Ulaş.2023-10-152023-10-152022PHYS 2022 A73https://digitalarchive.library.bogazici.edu.tr/handle/123456789/19817In this thesis, we will give a review of torsion-free Newton- Cartan theory. We will start by doing a large c expansion of general relativity and we will restrict ourselves to a few leading orders. After obtaining Newton-Cartan theory in this way, we will explore its symmetries. Through a special set of combined symmetries, we will construct a split space and time structure. Lastly, we will work out the field equations and equations of motion for a particle in the 3+1 formulation we have obtained.Mathematical physics.Newton-Cartan theory.x, 55 leaves