Real Algebraic Geometry is a field of mathematics that studies the geometry of real algebraic varieties, which are the solution sets of systems of polynomial equations with real coefficients. The conference "Real Algebraic Geometry" held in Rennes in 2011 marked the fourth in a series of international conferences that began in 1981. The conference aimed to celebrate the tradition of excellence in real algebraic geometry and to honor the contributions of key researchers such as Michel Coste, Louis Mahé, and Marie-Françoise Roy. The conference featured five surveys on real algebraic geometry, including topics such as algorithms in real algebraic geometry, topology of real algebraic varieties, analytic arcs and real analytic singularities, positive polynomials and sums of squares, and o-minimal structures. The conference also included abstracts and a list of participants. The surveys provided an overview of recent developments in the field, including algorithms for quantifier elimination, topological invariants of semi-algebraic sets, and numerical methods for polynomial optimization. The conference highlighted the importance of real algebraic geometry in various areas of mathematics and science, and emphasized the need for further research and development in the field.Real Algebraic Geometry is a field of mathematics that studies the geometry of real algebraic varieties, which are the solution sets of systems of polynomial equations with real coefficients. The conference "Real Algebraic Geometry" held in Rennes in 2011 marked the fourth in a series of international conferences that began in 1981. The conference aimed to celebrate the tradition of excellence in real algebraic geometry and to honor the contributions of key researchers such as Michel Coste, Louis Mahé, and Marie-Françoise Roy. The conference featured five surveys on real algebraic geometry, including topics such as algorithms in real algebraic geometry, topology of real algebraic varieties, analytic arcs and real analytic singularities, positive polynomials and sums of squares, and o-minimal structures. The conference also included abstracts and a list of participants. The surveys provided an overview of recent developments in the field, including algorithms for quantifier elimination, topological invariants of semi-algebraic sets, and numerical methods for polynomial optimization. The conference highlighted the importance of real algebraic geometry in various areas of mathematics and science, and emphasized the need for further research and development in the field.