In this tutorial, I will introduce a few basic principles and simple mathematical tools that were found useful in solving most problems involving causal inference in the health, social and behavioral sciences. The principles are based on non-parametric structural equation models, a natural generalization of those used by econometricians in the 1950-60s, yet cast in new mathematical and semantical underpinnings. This framework, enriched with a few ideas from logic and graph theory, gives rise to a friendly calculus of causes and counterfactuals that unifies all existing approaches to causation and enables rank and file researchers to handle complex problems in several of the sciences. These include questions of confounding, causal effect estimation, covariate selection, policy analysis, legal responsibility, mediation analysis, instrumental variables, measurement errors, selection bias, external validity and the integration of data from diverse studies.
Special emphasis will be placed on comparing the structural and potential-outcome approaches and, using illustrative examples, forming a symbiotic system that benefits from the strong features of both.