| The AdS/CFT correspondence has played an important role and has a widely use in string/M-theory. It is important to study the AdS/CFT correspondence in the cases with lower dimension space, since as a toy model, they are easier to handle for better understanding the correspondence. In this paper, we focus on the AdS2× S2 string, then generalize our results to other AdS string.Firstly, we review the supercoset method and AdS2× S2 string action. We also give the Maurer-Cartan equations based on the psu(1, 1|2) superalgebra and derive equations of motion of AdS2× S2 string, and the κ symmetry of AdS2× S2 string action is verified at the same time. Using the Nambu-Goto action of AdS2× S2 string, we present an alternative formulation for κ symmetry on target space.Secondly, by introducing the twisted dual transformation, we construct the flat currents, and conserved non-local charge with one free parameter A, for the superstring in AdS2× S2 background. Then we generalize our method to other AdS strings, such as AdS3× S3 string, AdS5× S5 string, and also noncritical string: AdS5× S1 string. In AdS5× S5 case, we find our method is equivalent to BPR's method, however, our tiwsted dual transformation is much more directly and efficiently, besides it's physical meaning is still unknown. In addiction, with the flat currents we give the famous Killing equation in AdS*× S*Thirdly, different with the KRR's method, we give the non-linear realization of the supergroup in G (x, y, θ) = g1 (θ) g2 (x)g3{y) form, which makes the calculation much more simple, then we simplify the AdS2× S2 string action in Killing gauge by fixing the κ symmetry. Also, we generalize this results to AdS5× S5 string and get the same form for the AdS5× S5 string action as that in the KRR's method. At last we present some related integrable field theory. Comparing to the case of 2D integrable field theory,we give the gauged WZNW action for Yang-Mills fields in four dimensional Minkowski space.
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