This chapter explores double integrals, extending the concept of integration from calculating areas under curves to determining volumes under three-dimensional surfaces. It begins with a comprehensive review of fundamental single-variable integration formulas, which serve as the building blocks for multivariable calculations. The text details the methods for evaluating integrals over both rectangular and general non-rectangular regions, emphasizing the importance of determining the correct order of integration. Key topics include the process of reversing the order of integration to simplify complex problems and the use of polar coordinates to evaluate integrals over circular or radial domains. Additionally, the chapter covers physical applications such as calculating mass and center of gravity and demonstrates how MATLAB can be utilized to perform symbolic integration and generate polar plots.