This is a Phase 1 clinical study to investigate the safety, pharmacokinetics, and pharmacodynamics of U3-1287 (AMG 888), a fully human monoclonal antibody targeting the HER3 receptor, in patients with advanced solid tumors. Eligible patients will have disease that is refractory or resistant to standard treatments or for which no standard therapy exists. The study will be conducted in two parts; a dose escalation (Part 1) and a dose expansion (Part 2). The hypothesis for this study is that U3-1287 (AMG888) will be safe and well tolerated in patients with advanced solid tumors and will show initial evidence of anti-tumor activity.