Under the supervision of Dr. Subhankar Mishra, I studied and drafted a thesis discussing differential privacy, pertinent techniques and algorithms, presented relevant mathematical analyses, discussed industrial deployments, and presented two recent pieces of literature in this field from NeurIPS 2021. Along with Dr. Mishra, my committee for this project also consisted Dr. Deepak Ku. Dalai, and Dr. Kamal Lochan Patra, both of whom are affiliated with the School of Mathematical Sciences, NISER, HBNI.