Inclusion Criteria:

          -  Participant must have AML not amenable to curative therapy, refractory to standard of
             care therapy or for which standard of care therapy does not exist. Participants who
             are candidates for stem cell transplantation must have been offered this therapeutic
             option.

          -  Must consent to provide biomarker analyses as described in the protocol.

          -  Must have an Eastern Cooperative Oncology Group (ECOG) Performance status of:

               -  Dose Escalation (Segment 1): 0 - 1

               -  Dose Expansion (Segment 2): 0 - 2

          -  Dose Escalation: Must have a serum albumin during Screening of >= 3.0 g/dL.

          -  Participant has adequate bone marrow, renal and hepatic function.

        Exclusion Criteria:

          -  Participant with known active Central Nervous System (CNS) disease.

          -  Participant has received anti-cancer traditional medicine or anti-cancer herbal
             remedies within 14 days prior to ABBV-744 dosing. Saw palmetto is considered
             anti-cancer herbal remedy. Participant has received anti-cancer therapy within a
             period of 14 days or 5 half-lives (whichever is longer; except for immunotherapy where
             a period of 21 days will be acceptable) prior to Study Day 1. Except for hydroxyurea
             which will be allowed during screening and treatment for controlling leukocytosis.

          -  Participant has been previously treated with a Bromodomain and Extra-Terminal (BET)
             inhibitor

          -  Participant has unresolved clinically significant toxicities from most recent prior
             anti-cancer therapy, defined as any Common Terminology Criteria for Adverse Events
             (CTCAE v 4.03) grade 2 or higher clinically significant toxicity (excluding alopecia).

          -  Participant has received the following within 7 days prior to the first dose of study
             drug: corticosteroid therapy, CYP3A inhibitors, CYP3A inducers.

          -  Participant consumed grapefruit or grapefruit products within 3 days prior to the
             first dose of study drug.

          -  Participant had major surgery within 28 days prior to Study Day 1.

          -  Participant is unable to swallow or absorb oral tablets.

          -  Participant has known infection with hepatitis B or hepatitis C.

          -  Participant has active peptic ulcer disease or other hemorrhagic
             esophagitis/gastritis, enteritis, colitis.

          -  Participant has symptoms of gross hematuria or gross hemoptysis

          -  Has electrocardiogram with a QT interval corrected for heart rate using Fridericia's
             formula (QTcF) > 470 msec or ECG with second degree type 2 or third degree
             atrioventricular block.