  We establish an explicit formula for the general solution of the Benjamin-Ono
equation on the torus and on the line. Contents 1. Introduction 1 1.1. The
Benjamin-Ono equation 1 1.2. The Lax pair 2 1.3. The explicit formula on the
torus 3 1.4. The explicit formula on the line 3 1.5. Organization of the paper
4 2. Proof of the explicit formula on the torus 4 3. Proof of the explicit
formula on the line 6 4. Final remarks 8 References 9
