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The fourth Workshop on Numerical and Observational Astrophysics organized by the Numerical Astrophysics Group of IAFE is framed at the dawn of the era of the so-called “Big Data”. The unprecedented amount of high precision data that are being obtained, and will be obtained in the very near future, throughout the new generation of telescopes, will give us a new vision of our Galaxy and the Universe: a detailed description of stellar populations (RAVE, SEGUE, LAMOST, GAIA), interstellar and intergalactic media (ALMA, GASKAP), the chemical and dynamic properties of galaxies at different stages of evolution (ALMA, ELT, LSST). The LSST by itself will gather in one day of operation the total volume of data obtained by the Sloan Digital Sky Survey. In this context, it is essential to develop new tools for processing and analysis. Numerical simulations provide the necessary nexus between the theoretical models for structure formation and the observational data. New synthetic universes capable of reproducing the unprecedented amount of observational data to come and also new tools for the analysis, are needed. We aim at providing a great environment for fruitful discussions and also give the opportunity for young scientists and PhD students to interact with leading scientists in areas related to formation and evolution of galaxies, both from the observational an theoretical point of view. The meeting will include extended talks that will provide a detailed overview of the state of the art regarding modeling and data processing tools.