The Kawahara equation has fewer symmetries than the KdV equation; in particular, it has no invariant scaling transform and is not completely integrable. Thus its analysis requires different methods. We prove that the Kawahara equation is locally well posed in H-7/4, using the ideas of an F?stype space . Then we show that the equation is globally well posed in Hs for s ? -7/4, using the ideas of the I-method .