This is a joint session of the courses "Approximation Algortithms" and "Discrepancy Theory". I just post it here in case it may be interesting to a broader audience. I will talk about a variant of randomized rounding (sometimes calles LP-based rounding) that got some attention recently. Instead of rounding the variables independently, we now try to incorporate suitable dependencies. I will try to cover Srinivasan's FOCS 2001 and 2002 papers as well as some own work. I will review the very basics of independent randomized rounding in case you missed Khaled's lecture last time.