Inclusion Criteria:

• Male or Female ≥ 18 years old
• Diagnosed hematologic malignancy (other than lymphoma) that has relapsed or is refractory to standard care or for which no standard care is available or acceptable
• Able to give written informed consent
• ECOG performance status ≤ 2
• BSA ≥ 1.5 m² (first cohort only)
• Minimum life expectancy of 3 months or more
• Adequate renal function
• Adequate hepatic function
• Ability to comply with study procedures in the Investigator's opinion
• Adequate cardiac function
• For females of childbearing potential, a negative pregnancy test must be documented prior to enrollment
• Female patients who are of childbearing potential must agree to use an effective form of contraception with their sexual partners throughout participation in this study

Exclusion Criteria:

• Have had cytotoxic chemotherapy or radiotherapy within 21 days prior to entering the study, or those who have not recovered from adverse events due to agents administered more than 28 days earlier with the exception of alopecia
• Received any other investigational agents or have received an investigational agent within 14 days of starting AP24534
• Malabsorption syndrome or other illness which could effect oral absorption
• Significant uncontrolled cardiac disease
• Uncontrolled hypertension
• Uncontrolled intercurrent illness
• Pregnant
• Known infection of HIV
• Autologous or allogeneic stem cell transplant < 3 months prior to enrollment; any evidence of ongoing GVHD, or GVHD requiring immunosuppressive therapy
• Another primary malignancy within the past 3 years
• Any condition or illness which, in the opinion of the investigator, would compromise patient safety or interfere with the evaluation of the safety of the drug
• Patients taking medicinal products that are known to be associated with prolongation of the QT interval on the electrocardiogram
• Major surgery (with the exception of intravenous catheter placement or bone marrow biopsy) within 14 days prior to initiating AP24534 therapy