by SDEs with jumps where the drift coefficient is one-sided Lipschitz and satisfies the polynomial growth condition. For such equations, it is proved in [@Martin3] that Euler explicit method fails to converge strongly to the exact solution while Euler implicit method converges strongly, but requires much computational efforts. Recently, a new explicit and efficient method was developed in [@Martin1] called tamed Euler scheme. In [@Martin1], the authors proved that the tamed Euler converges strongly with order 0.5 to the exact solution of SDEs under non-global Lipschitz condition. In this thesis, we extend the tamed Euler scheme by introducing a compensated tamed Euler scheme for SDEs with jumps. We prove that this scheme converges strongly with standard order $0.5$. We also extend the semi-tamed Euler developed in [@Xia2] and we prove that this scheme converge strongly with order $0.5$ for SDEs with jumps. As a consequence of this latter result, we prove the strong convergence of the tamed Euler scheme for SDEs with jumps. The stability analysis of both tamed Euler and semi-tamed Euler are done in this thesis.

This thesis is organized as follows. In chapter 1, we recall some basic notions in probability theory and stochastic process. Chapter 2 