I will first take about 45 minutes to talk about the background of isometric embedding and outline of my 6-hour talks about our work on global   Nash-Kuiper theorems and Monge-Ampere equation.
Then I will take the rest time to give the presentation about the celebrated Nash-Kuiper theorem and its proof.

Basic theory about Rieman manifold, PDE, and functional analysis

[1] N.H. Kuiper. On C^1 isometric embeddings. I, II. Nederl. Akad. Wetensch. Proc. Ser. A. 58= Indag. Math. 17: 545-556, 683-689, 1955;
[2] J. Nash. C^1 isometric embeddings. Ann. of Math. (2), 60: 383-396, 1954;
[3] L. Szekelyhiidi, From isometric embedding to turbulence, HCDTE lecture notes. Part II. Nonlinear hyperbolic PDEs, dispersive and transport equations / G. Alberti.. (eds.) Springfield : AIMS, 2013. - P. 195 - 255.