This course provides an advanced introduction to modern quantitative causal inference in the social sciences. The class covers the canonical approaches to causal inference and includes excursions to the leading edge of the field. We begin with a foundational introduction to both the potential outcomes and graphical frameworks for causality, before considering a range of applied research designs for causal inference. We first discuss identification and estimation for classical randomized experiments, with brief forays into more complex designs. We then turn to a range of observational designs, which will be the primary focus of the class. The first of these is selection on observables (SOO), and we cover regression, matching, and weighting as estimations strategies, before discussing sensitivity analyses and interval estimation (bounds). We then consider instrumental variables (IV) from both the modern potential outcomes perspective and, briefly, the classical structural approach, before delving into new IV settings like examiner designs, shift-share designs, and recentered instruments. From IV we move to regression discontinuity designs (RDD); we approach identification from the continuity perspective and introduce local polynomial approximation for estimation. Finally, we pivot to causal inference with time-varying data, focusing first on the canonical two-period difference-in-differences (DiD) design. We then consider generalised DiD with many time periods, treatment effect heterogeneity, staggered assignment, and non-absorbing treatments. Throughout the class examples are drawn from different social sciences. The course includes seminars for each of the major methods, which combine the close reading and discussion of an applied paper with a brief session on implementation in R.