Economics helps us to understand that certain slick mechanisms are operating beyond what we see in our daily economic lives. To fully understand and appreciate those mechanisms, we need to master the core mathematical theories, some of which are highly advanced and typically covered in a graduate course. This textbook presents those theories without compromising rigor, but at the same time, the author offers a number of innovative pedagogical twists that make the difficult materials completely accessible to undergraduate students and even to general readers. Written in a chatty, colloquial style, the author explains basic messages and core insights that are usually hidden between the lines. The usefulness of these theories are shown through a number of real-life examples, and in the end, the readers can see that the mathematical models provide deep insights into social justice and philosophy. This book helps readers to think like an economist.