The weight filtration for real algebraic varieties

29 pages. MSRI Publications, \textbf{18} "Topology of Stratified Spaces" (2011), 121--160Using the work of Guillen and Navarro Aznar we associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on Borel-Moore homology with Z/2 coefficients an analog of the weight filtration for complex algebraic varieties