Chapters; 1. Introduction; 2. Preliminaries; 3. Statement of the gluing theorem; 4. Proof of the gluing theorem I: Cut-off functions and weighted Sobolev norm; 5. Proof of the gluing theorem II: Gluing by alternating method; 6. Exponential decay of $T$ derivatives; 7. Surjectivity and injectivity of the gluing map; 8.

Exponential decay estimate implies smoothness of coordinate change; A. Error term estimate of non-linear Cauchy-Riemann equation I; B. Estimate of Parallel transport 1; C. Error term estimate of non-linear Cauchy-Riemann equation II; D. Estimate of Parallel transport 2; E. Estimate of the non-linearity of Exponential map; F. Estimate of Parallel transport 3; G. Estimate of $T$ derivative of the error term of non-linear Cauchy-Riemann equation; H.

Proof of Lemma.