This is a first-in-man trial, in which BYL719 will be administered to adult patients with advanced solid tumors, whose tumors have an alteration of the PIK3CA gene and whose disease has progressed despite standard therapy or for whom no standard therapy exists. A combination of BYL719 with fulvestrant will also be investigated in post-menopausal patients with locally advanced or metastatic breast cancer whose tumors have an alteration of the PIK3CA gene. The single agent MTD dose expansion cohort and the fulvestrant combination MTD dose expansion cohort will also include ER+/HER2- breast cancer patients whose tumors have the wild type PIK3CA gene