The chapter presents fundamental concepts and theories regarding airfoil lift and drag generation. It begins by presenting crucial definitions for use in airfoil theory. Ranging from the basics of Buckingham’s Π-theory to representation of forces moments to discussion of pressure distribution along the upper and lower surfaces of the airfoil and how it affects the growth of the boundary layer and, eventually, flow separation. Discussion of airfoil stall characteristics and ice-accretion problems are introduced with the basics of airfoil design theory. Then important geometric properties of airfoils are presented to help make the aircraft designer better rounded when comes to identifying various airfoil types, such as NACA airfoils, and understanding of their background. For this purpose, the section introduces a number of airfoils that have gained fame or notoriety in the history of aviation. This is followed by a discussion of the generation of forces and moments on the airfoil and how various outside agents, such as very high airspeeds, high angle-of-attack, deflection of control surfaces, and even surface contamination, affects their aerodynamic properties. Finally, it presents a method to help the designer select the proper airfoil for a new aircraft design.