 The study will be an open label, multicenter, dose finding study. Depending on the tolerated dose up to 7 dose levels will be explored in this study, approximately 33 patients 21-54 depending on number of cohorts may be enrolled into this study. Three patients will be initially dosed in each cohort. The primary objective of this study is to determine the recommended dose RD of twice daily oral doses of AZD2281 either as intermittent therapy for 7 days out of a 28-day schedule or given continuously, administered in combination with liposomal doxorubicin to patients with advanced solid tumors. 