Explore the fundamentals of differential privacy in this comprehensive tutorial led by Dr. Borja Balle from Amazon Research. Delve into key definitions, intuitions, and core building blocks used in differentially private mechanisms. Learn about privacy-preserving computations on sensitive data, various applications in machine learning, and different variants of differential privacy. Gain insights into the roles these definitions play in practical applications. Discover the importance of mathematical frameworks in studying privacy, dimensionality, resolution, and expectations. Examine concepts such as randomized response, output perturbation mechanisms, and the exponential mechanism. This 1-hour 49-minute seminar, part of the Alan Turing Institute's interest group on Privacy-Preserving Data Analysis, offers a comprehensive introduction to this crucial aspect of data science and machine learning.