Study of Acalabrutinib Alone or in Combination Therapy in Subjects With B-cell Non-Hodgkin Lymphoma

Inclusion Criteria:

* Men and women ≥ 18 years of age.
* Part 1: A confirmed diagnosis of FL Grade 1, 2, or 3a, which has relapsed after, or been refractory to ≥ 1 prior therapy for FL, or subjects who have not previously received systemic anticancer therapy for FL., and which requires treatment.
* Part 2: For subject with relapsed or refractory MZL:

Histologically confirmed MZL including splenic, nodal, and extranodal sub-types

1. Subjects with splenic MZL must have an additional measurable lesion, nodal or extranodal, as described in inclusion criterion #4;
2. Subjects with gastric mucosa-associated lymphoid tissue (MALT) lymphoma must be Helicobacter pylori (HP)-negative

   * Part 3: For subjects with FL: Pathologically confirmed diagnosis of FL Grade 1, 2, or 3a, which has relapsed after, or been refractory to ≥ 1 prior therapy for FL and which requires treatment per National Cancer Institute or ESMO clinical practice guidelines.
   * Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2.
   * Agreement to use contraception during the study and for 30 days after the last dose of study drugs if sexually active and able to bear or beget children.

Exclusion Criteria:

* •A life-threatening illness, medical condition or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of acalabrutinib, or put the study outcomes at undue risk
* Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any Class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification, or Qtc \>480 msec
* Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel, gastric bypass, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction.
* Breast feeding or pregnant