XtremWeb : the Open Source Platform for Desktop Grids. XtremWeb is an open source software to build lightweight Desktop Grid by gathering the unused resources of Desktop Computers (CPU, storage, network). Its primary features permit multi-users, multi-applications and cross-domains deployments. XtremWeb turns a set of volatile resources spread over LAN or Internet into a runtime environment executing highly parallel applications. Every day, XtremWeb provides computing power to scientists to run their code in High Energy Phisics, BioMolecuar, Mathematics and many more scientific or industrial domains. XtremWeb is highly programmable and customizable a wide range of applications (bag-of tasks, master/worker), of computing requirements (data/CPU/network-intensive) and computing infrastructures (clusters, Desktop PCs, multi-Lan) in a manageable, scalable and secure fasion. The XtremWeb is also a research in Grid and P2P technologies. Our team is working on improving security, efficiency, dependability of this promising new computing paradigm. XtremWeb is supported by national grants and by major European grants around Grid and Desktop Grid such as FP6 CoreGrid: European Network of Excellence and the FP7 EDGeS : Enabling Desktop Grid for E-Science.