The purpose of this study is 2-fold: initially, in the dose escalation phase, the goal is to determine the safety profile of orally administered AP26113, including: the maximum tolerated dose (MTD), dose limiting toxicities (DLTs), recommended phase 2 dose (RP2D), and pharmacokinetic (PK) profile. Then, once the RP2D is established, an expansion phase will assess the preliminary anti-tumor activity of AP26113, both in non-small cell lung cancer (NSCLC) with ALK gene rearrangement or mutated EGFR, and in other cancers with abnormal targets against which AP26113 is active. Approximately 110 to 130 patients will be enrolled.