This book contains review articles of most of the topics addressed at the conf- ence on Simulations of Magnetohydrodynamic turbulence in astrophysics: recent achievements and perspectives which took place from July 2 to 6, 2001 at the Institut Henri Poincar¿e in Paris. We made the choice to publish these lectures in a tutorial form so that they can be read by a broad audience. As a result, this book does not give an exhaustive view of all the subjects addressed during the conference. The main objective of this workshop which gathered about 90 scientists from di?erent ?elds, was to present and confront recent results on the topic of t- bulence in magnetized astrophysical environments. A second objective was to discuss the latest generation of numerical codes, such as those using adaptive mesh re?nement (AMR) techniques. During a plenary discussion at the end of the workshop discussions were held on several topics, often at the heart of vivid controversies. Topics included the timescale for the dissipation of magneto-hydrodynamical (MHD) turbulence, the role of boundary conditions, the characteristics of imbalanced turbulence, the validity of the polytropic approach to Alfv¿en waves support within interst- lar clouds, the source of turbulence inside clouds devoid of stellar activity, the timescale for star formation, the Alfv¿en Mach number of interstellar gas motions, the formation process for helical ?elds in the interstellar medium. The impact of small upon large scales was also discussed.

MHD Turbulence.- The Evolving Phenomenological View on Magnetohydrodynamic Turbulence.- Coronal Heating and Reduced MHD.- MHD Turbulence: Scaling Laws and Astrophysical Implications.- Numerical Approches.- Numerical Simulations of Magnetic Fields in Astrophysical Turbulence.- Adaptive Mesh Refinement in MHD Modeling. Realization, Tests and Application.- Turbulence in the ISM.- Observations of Interstellar Magnetic Fields.- MHD Turbulence in Star-Forming Regions and the Interstellar Medium.- Thermal Instability and Magnetic Pressure in the Turbulent Interstellar Medium.- Developing Diagnostics of Molecular Clouds Using Numerical MHD Simulations.- Star Formation and the Initial Mass Function.- The Structure and Dynamics of Filamentary Molecular Clouds.- Numerical Simulations of MHD Turbulence in Accretion Disks.- Current Issues in Reconnection and Astrophysical Dynamos.- Recent Developments in Collisionless Reconnection Theory: Applications to Laboratory and Astrophysical Plasmas.- Problems and Progress in Astrophysical Dynamos.- The Helicity Issue in Large Scale Dynamos.- Recent Developments in Magnetic Dynamo Theory.