Part 1 is a dose-escalation study to establish the maximum tolerated dose based on dose-limiting toxicities and to evaluate the safety and tolerability of multiple doses of Andes-1537 for Injection in patients with advanced unresectable solid tumors that are refractory to standard therapy or for which no standard therapy is available. Part 2 is an open-label, dose-expansion study to determine the safety, tolerability, and preliminary efficacy of Andes-1537 in patients with advanced solid tumors. In part 2, patients will be enrolled and receive the recommended phase 2 dose established in part 1 based on the safety, tolerability, pharmacokinetics, and preliminary efficacy data.