This is a review article on pseudo-holomorphic curves which attempts at touching all the main analytical results. The goal is to make a user friendly introduction which is accessible to those without an analytical background. Indeed, the major accomplishment of this review is probably its short length.
Nothing in here is original and can be found in more detailed accounts such as  and . The exposition of the compactness theorem is somewhat different from that in the standard references and parts of it are imported from harmonic map theory , . The references used are listed, but of course any mistake is my own fault.
 Agmon, Shmuel. Lectures on exponential decay of solutions of second-order elliptic equations: Bounds on eigenfunctions of n-body Schrodinger operations.(mn-29). Vol. 29. Princeton University Press, 2014.10.2307/j.ctt13x1d8zSearch in Google Scholar
 D. McDuff, and D. Salamon, J-holomorphic curves and symplectic topology. Vol. 52. American Mathematical Soc., 2012.Search in Google Scholar
 Sacks, J., and K. Uhlenbeck. The existence of minimal immersions of two-spheres. Bulletin of the American Mathematical Society 83.5 (1977): 1033-1036.10.1090/S0002-9904-1977-14366-8Search in Google Scholar
 Wendl, Chris. Lectures on holomorphic curves in symplectic and contact geometry. arXiv preprint arXiv:1011.1690 (2010).Search in Google Scholar
© 2020 Gonçalo Oliveira, published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.