Essential Mathematics for Political and Social Research addresses an educational deficiency in the social and behavioral sciences. This is the first book of its kind to specifically address the comprehensive introduction to the mathematical principles needed by modern social scientists. The material introduces basic mathematical principles necessary to do analytical work in the social sciences, starting from first principles, but without unnecessary complexity. The core purpose is to present fundamental notions in standard notation and standard language with a clear, unified framework throughout. Through examples and exercises, this book is intended to not only motivate specific mathematical principles and practices, but also introduce the way that social science researchers use these tools. The intended emphasis is on conceptual understanding of key principles and their subsequent application.