Stability of line solitons for the KP-II equation in R2

* Introduction* The Miura transformation and resonant modes of the linearized operator* Semigroup estimates for the linearized KP-II equation* Preliminaries* Decomposition of the perturbed line soliton* Modulation equations* A priori estimates for the local speed and the local phase shift* The $L^2(\mathbb{R}^2)$ estimate* Decay estimates in the exponentially weighted space* Proof of Theorem 1.1* Proof of Theorem 1.4* Proof of Theorem 1.5* Appendix A. Proof of Lemma 6.1* Appendix B. Operator norms of $S^j_k$ and $\widetilde{C_k}$* Appendix C. Proofs of Claims 6.2, 6.3 and 7.1* Appendix D. Estimates of $R^k$* Appendix E. Local well-posedness in exponentially weighted space* Bibliography