Inclusion Criteria:

        Chemotherapy and immunotherapy-naïve, symptomatic and in need of treatment patients, with
        histologically proven CD20-positive MZL, not eligible for local therapy, including:

          1. EMZL (MALT Lymphoma) patients with MALT- IPI score 1-2 in need of systemic therapy.

             Either de novo or relapsed following local therapy (including surgery, radiotherapy
             and antibiotics for H. pylori-positive gastric lymphoma) arisen at any extranodal site
             with MALT-international prognostic index (IPI) score 1-2 at the time of study entry.

             1.1.The following patients with gastric MALT Lymphoma can be entered:

               1. H. pylori-negative cases, either de novo (non pretreated) or at relapse following
                  local therapy (i.e., surgery, radiotherapy or antibiotics).

               2. H. pylori-positive cases at diagnosis, who either first line antibiotics or
                  further local treatment (surgery or radiotherapy), including patients with:

                    -  clinical (endoscopic) and histological evidence of disease progression at
                       any time post H. pylori eradication;

                    -  clinical (endoscopic) and histological relapse (without H. pylori
                       re-infection), after a remission patients;

                    -  persistent (stable) lymphoma at ≥ 1 year post H. pylori eradication. 1.2.
                       Similar consideration may be applied to patients with ocular adnexal
                       lymphoma treated with antibiotics.

          2. SMZL patients in need of therapy. Either de novo or relapsed following local therapy
             [including surgery and antiviral therapy for Hepatitis C virus (HCV)]. Patient must
             have a symptomatic disease requiring treatment and be not eligible for splenectomy or
             not willing to undergo splenectomy.

             2.1. Patients with SMZL can be entered if any of the following criteria is present:

               1. bulky progressive or painful splenomegaly;

               2. enlarged lymph nodes or involvement of extranodal sites with or without
                  cytopenias , i.e. involvement of ≥3 nodal sites, each with a diameter of ≥3 cm.
                  Any nodal tumor mass with a diameter of ≥7 cm (GELG criteria, as adopted in
                  follicular lymphoma);

               3. one of the following symptomatic/progressive cytopenias:

                    -  Hgb < 10 g/dL;

                    -  ANC < 1000/μL:

                    -  PLT< 80 000/μL whatever the reason (autoimmune or hypersplenism or bone
                       marrow infiltration).

             2.2. Splenectomised patients with rapidly raising lymphocyte counts, lymphadenopathy
             or involvement of extranodal sites can be entered.

             2.3. SMZL with concomitant HCV infection who have not responded to or are relapsed
             after antiviral therapy can be entered.

          3. NMZL patients in need of therapy Either, de novo presenting with disseminated disease
             or relapsed after local radiotherapy or following antiviral therapy for HCV. Localized
             nodal MZL is not eligible.

               -  Measurable or evaluable disease.

               -  Ann Arbor II-IV. Stage I disease may be eligible only if not candidate to local
                  therapy (surgery or radiotherapy).

               -  Age ≥ 18.

               -  Life expectancy of at least 1 year.

               -  ECOG Performance status 0-2.

               -  Adequate bone marrow, kidney and liver function

               -  For women of childbearing potential only: negative serum pregnancy test done
                  within 7 days prior to study drugs administration or within 14 days if with a
                  confirmatory urine pregnancy test within 7 days prior to the first study drugs
                  administration.

               -  Fertile male or female patients of childbearing potential and their partners must
                  use higly effective contraception methods during the study and for at least 12
                  months after the last dose of subcutaneous rituximab. In case hormonal methods of
                  birth control is used a barrier method must be added.

               -  Ability to understand and the willingness to sign a written informed consent
                  document

        Exclusion Criteria:

          1. Any type of lymphoma other than MZL (including MZL with histologic transformation to
             high-grade lymphoma).

          2. Localized (stage IE and IIE) MALT lymphoma, for example gastric, ocular and cutaneous
             lymphoma, that may benefit from local therapy only (surgery or radiotherapy).

          3. Known CNS involvement of MZL.

          4. Any previous systemic treatment with immunotherapy or chemotherapy or with BTK
             inhibitors.

          5. Major surgery within 4 weeks prior to registration.

          6. History of stroke or intracranial bleeding within 6 months.

          7. Known bleeding diathesis (eg, von Willebrand's disease) or hemophilia.

          8. Concurrent use of warfarin of other vitamin K antagonists.

          9. Concurrent use of strong cytochrome P450 (CYP)3A4/5 inhibitors (see
             http://medicine.iupui.edu/clinpharm/ddis/clinical-table/).

         10. Any 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 ibrutinib capsules, or put the study outcomes at undue
             risk.

         11. International normalized ratio (INR) or prothrombin time (PT) ≥1.5 ULN. Partial
             thromboplastin time (PTT) or activated PTT (aPTT) ≥1.5 ULN unless due to lupus
             anticoagulant.

         12. Vaccinated with live, attenuated vaccines within 4 weeks prior to randomization.

         13. Clinically significant hypersensitivity (e.g., anaphylactic or anaphylactoid reactions
             to the compound of ibrutinib and/or rituximab themselves or to the excipients in their
             formulation).

         14. Positive test results for chronic HBV infection (defined as positive HBsAg serology).

         15. Patients with occult or prior HBV infection (defined as negative HBsAg and positive
             total HBcAb) may be included if HBV DNA is undetectable, provided that they are
             willing to undergo monthly DNA testing and taking specific antiviral prophylaxis,
             according to local policy. Patients who have protective titers of hepatitis B surface
             antibody (HBsAb) after vaccination are eligible.

         16. Positive test results for hepatitis C. Patients positive for HCV antibody are eligible
             only if PCR is negative for HCV RNA.

         17. HIV infection or immunodeficiency.

         18. Active, severe infections

         19. Pregnancy or breastfeeding.

         20. Clinically significant cardiovascular diseases such as uncontrolled or symptomatic
             arrhythmias, congestive heart failure, or myocardial infarction within 6 months of
             screening, or any Class 3 (moderate) or Class 4 (severe) cardiac disease as defined by
             the New York Heart Association Functional Classification.

         21. Any serious medical or psychiatric illness likely to interfere with participation in
             this clinical study.

         22. Prior history of malignancies other than MZL within 3 years,with the exception of
             adequately treated cervical carcinoma in situ or localized non-melanoma skin cancer.

         23. Current enrolment or participation in another therapeutic clinical trial within 28
             days prior to treatment start