Causal inference is a fundamental goal of social research, and it has been a topic of methodological research for decades. The evaluation of social science theory cannot proceed without assessing the sizes of entailed cause-effect relationships. Policy research cannot be conducted without estimating the impacts that follow from policy interventions. Unfortunately, for most social science research, controlled experimentation is not possible. And, when experimentation is feasible, it is often only possible in artificial contexts and for subjects who are not the representative of the target populations for inference. Tremendous progress has been made in the past 15 years in the causal analysis of non-experimental data, also known as observational data. The proposed handbook aims to explain this progress and then demonstrate how to use state-of-the-art methods for causal analysis in basic and applied empirical scholarship. The methods involve defining causal contrasts using counterfactual definitions and then estimating differences across individuals while maintaining clear assumptions about these contrasts. This approach allows for advanced forms of regression and multivariate case-matching, as well longitudinal differencing techniques, and instrumental variable estimation based on the occurrence of natural experiments. In the tradition that will be explicated in this handbook, substantial attention will also be devoted to representing underlying assumptions using causal graphs.