We give a new construction of Teichmueller space by patching together Kuranishi families. Teichmueller space is constructed directly as a complex manifold, and the construction makes it obvious that it enjoys a natural universal property; it is also very easy to show that the action of the Teichmueller modular group on Teichmueller space is properly discontinuous. We also discuss the basic properties of Teichmueller space, and in particular show that our construction leads to significant simplifications in the proof of the fundamental theorem asserting that the genus g Teichmueller space is homeomorphic to a (6g - 6)-dimensional ball.