Inclusion Criteria:

          1. Written informed consent obtained from the subject prior to performing any
             protocol-related procedures, including screening evaluations

          2. Age >/= 18 years at time of study entry

          3. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

          4. Adequate normal organ and marrow function as defined below:

             Hemoglobin ≥ 9.0 g/dL Absolute neutrophil count (ANC) ≥ 1.5 × 109/L (> 1500 per mm3)
             Platelet count ≥ 100 × 109/L (>100,000 per mm3) Serum bilirubin ≤ 1.5× institutional
             upper limit of normal (ULN)AST<3.0 Creatinine clearance >50mL/miN Aspartate
             transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 × ULN (≤ 5 × ULN if documented
             liver metastasis are present); Serum creatinine ≤ 2.0 mg/dL or calculated creatinine
             clearance ≥ 50 mL/min as determined by the Cockcroft-Gault equation;

             Males:

             Creatinine CL (mL/min) = Weight (kg) × (140 - Age) 72 × serum creatinine (mg/dL)

             Females:

             Creatinine CL (mL/min) = Weight (kg) × (140 - Age) × 0.85 72 × serum creatinine
             (mg/dL)

          5. Female subjects must either be of non-reproductive potential (i.e., post-menopausal by
             history: ≥60 years old and no menses for >/=1 year without an alternative medical
             cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history
             of bilateral oophorectomy) or must have a negative serum pregnancy test upon study
             entry.

          6. Subject is willing and able to comply with the protocol for the duration of the study
             including undergoing treatment and scheduled visits and examinations including follow
             up.

          7. Surgically resectable MPM with no disease extension beyond the ipsilateral hemithorax

          8. Planned resectional surgery for MPM [extrapleural pneumonectomy (EPP) or pleurectomy
             and decortication (P/D)]

          9. Any MPM histology (epithelial, mixed, sarcomatoid)

         10. N0 or N1 nodal disease as present on perioperative chest CT and/or PET CT.

         11. N2 nodal disease if no progression after 2 cycles of standard chemotherapy.
             Progression will be considered if additional N1 or N2 disease develop during
             chemotherapy

        Exclusion Criteria:

          1. Involvement in the planning and/or conduct of the study (applies to both AstraZeneca
             staff and/or staff at the study site) or previous enrollment or randomization in the
             present study

          2. Participation in another clinical study with an investigational product during the
             last 3 months

          3. Any previous treatment with a PD1 or PD-L1 inhibitor, including MEDI4736

          4. Receipt of the last dose of anti-cancer therapy (chemotherapy, immunotherapy,
             endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal
             antibodies, other investigational agent) 30 days prior to the first dose of study
             drug, and 30 days prior to the first dose of study drug for subjects who have received
             prior TKIs [e.g., erlotinib, gefitinib and crizotinib] and within 6 weeks for
             nitrosourea or mitomycin C).

          5. Current or prior use of immunosuppressive medication within 28 days before the
             infusion with MEDI4736 or MEDI4736 + tremelimumab and through 90 days post infusion,
             with the exceptions of intranasal and inhaled corticosteroids or systemic
             corticosteroids at physiological doses, which are not to exceed 10 mg/day of
             prednisone, or an equivalent corticosteroid.

          6. Any unresolved toxicity (>CTCAE grade 2) from previous anti-cancer therapy.

          7. Any prior Grade ≥3 immune-related adverse event (irAE) while receiving any previous
             immunotherapy agent, or any unresolved irAE >Grade 1

          8. Active or prior documented autoimmune disease within the past 2 years NOTE: Subjects
             with vitiligo, Grave's disease, or psoriasis not requiring systemic treatment (within
             the past 2 years) are not excluded.

          9. Active or prior documented inflammatory bowel disease (e.g., Crohn's disease,
             ulcerative colitis)

         10. History of primary immunodeficiency

         11. History of allogeneic organ transplant

         12. History of hypersensitivity to MEDI4736 or any excipient

         13. History of hypersensitivity to tremelimumab or the combination of MEDI4736 +
             tremelimumab

         14. Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable
             angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, active
             bleeding diatheses including any subject known to have evidence of acute or chronic
             hepatitis B, hepatitis C or human immunodeficiency virus (HIV), or psychiatric
             illness/social situations that would limit compliance with study requirements or
             compromise the ability of the subject to give written informed consent

         15. Known history of previous clinical diagnosis of tuberculosis

         16. History of leptomeningeal carcinomatosis

         17. Receipt of live attenuated vaccination within 30 days prior to study entry or within 6
             months of receiving MEDI4736 or MEDI + tremelimumab

         18. Receipt of drugs with laxative properties and herbal or natural remedies for
             constipation within 90 days of receiving MEDI4736 or MEDI + tremelimumab

         19. Receipt of sunitinib within 3 months of receiving tremelimumab

         20. Female subjects who are pregnant, breastfeeding, or male or female subjects of
             reproductive potential who are not employing an effective method of birth control

         21. Any condition that, in the opinion of the investigator, would interfere with the
             evaluation of the study treatment or interpretation of subject safety or study results

         22. Symptomatic or uncontrolled brain metastases requiring concurrent treatment, inclusive
             of but not limited to surgery, radiation, and/or corticosteroids.

         23. Subjects with uncontrolled seizures

         24. N3 nodal disease

         25. History of interstitial lung disease/pneumonitis

         26. No tissue is obtainable at the time of thoracoscopy.