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In this book, we present some WENO schemes for solving hyperbolic conservation laws in one and two dimensions, scalar and vector problems. WENO methods give very high accuracy results and non-oscillatory profiles. Here we give fifth, seventh and ninth order methods. Also we proposed the seventh order Hermite WENO method. We use also Runge-Kutta methods for time integration. The presented different schemes are superior to the other classical WENO schemes.