This text contains the mathematical material necessary as background for the topics covered in advanced microeconomics courses. It focuses on two key components of microeconomics - optimization subject to constraints and the development of comparative statistics. Assuming familiarity with calculus of one variable and basic linear algebra, the text allows more extensive coverage of additional topics like constrained optimization, the chain rule, Taylor's theorem, line integrals and dynamic programming. It contains numerous examples that illustrate economics and mathematical situations, many with complex solutions.