We propose a theory for the drying of liquid droplets of surfactant solutions. We show that the added surfactant hinders droplet receding and facilitates droplet spreading, causing a complex behavior of the contact line of an evaporating droplet: the contact line first recedes, then advances, and finally recedes again. We also show that the surfactant can change the deposition pattern from mountain-like to volcano-like and then to coffee-ring-like. Specially, when the contact line motion undergoes a clear receding-advancing transition, a two-ring pattern is formed. The mechanism of the two-ring formation is different from the stick-slip mechanism proposed previously and may be tested experimentally.