Inclusion Criteria:

          -  Men and women ≥ 18 years old

          -  Primary tumor amenable to safe research biopsy. A tumor biopsy is required for study
             entry.

          -  Histology proven epithelial or biphasic MPM

               -  Diagnostic core biopsy specimens must be reviewed by faculty pathologist at SKCC,
                  MDACC, or UMGCCC.

               -  Either a formalin fixed paraffin block that has been confirmed by a pathologist
                  to contain tumor or a minimum of twenty 5-micron tissue sections (slides) of
                  tumor biopsy sample must be available for biomarker evaluation (study pathologist
                  must review for adequacy of sampling). This can be obtained from archived tissues
                  if adequate, or from a new biopsy as needed.

          -  Stage I-III and deemed to be potentially surgically resectable as assessed by faculty
             surgeon at SKCC, MDACC, or UMGCCC

          -  ECOG performance status 0-1

          -  Adequate organ function as follows:

               -  Leukocytes ≥ 2,000/mm3

               -  Absolute neutrophil count (ANC) ≥ 1000/mm3

               -  Platelet count ≥ 100,000/mm3

               -  Hemoglobin ≥ 9 g/Dl

               -  Creatinine ≤ 1.5 x ULN or creatinine clearance (CrCl) ≥40 mL/min (if using the
                  Cockcroft-Gault formula below):

        Female CrCl = (140 - age in years) x weight in kg x 0.85 72 x serum creatinine in mg/dL

        Male CrCl = (140 - age in years) x weight in kg x 1.00 72 x serum creatinine in mg/dL

          -  Total Bilirubin ≤ 1.5 x institutional ULN (except subjects with Gilbert Syndrome, who
             can have total bilirubin < 3.0 mg/dL)

          -  AST(SGOT), ALT(SGPT), and alkaline phosphatase ≤ 3 times the institutional upper limit
             of normal

          -  Subjects must have adequate lung function to permit surgical resection determined by
             pre-enrollment pulmonary function tests to include DLCO

               -  The effects of nivolumab on the developing human fetus are unknown. For this
                  reason, women of child-bearing potential (WOCBP) and men must agree to use
                  adequate contraception (hormonal or barrier method of birth control; abstinence)
                  prior to study entry and for the duration of study participation and for up to 23
                  weeks after the last dose of nivolumab. Should a woman become pregnant or suspect
                  she is pregnant while she or her partner is participating in this study, she
                  should inform her treating physician immediately. Sexually active fertile men
                  must use effective barrier birth control if their partners are WOCBP for up to 31
                  weeks after the last dose of nivolumab. WOCBP must have a negative serum or urine
                  pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within
                  two weeks of registration. Women must not be breastfeeding.

               -  Patient understands the study regimen, its requirements, risks and discomforts
                  and is able and willing to sign the informed consent form. Voluntary signed and
                  dated IRB/IEC approved written informed consent form in accordance with
                  regulatory and institutional guidelines must be obtained before the performance
                  of any protocol related procedures that are not part of normal patient care.
                  Subjects must be competent to report AEs, understand the drug dosing schedule and
                  use of medications to control AEs.

        Exclusion Criteria:

          -  Stage I-III disease but deemed to be unresectable, a poor surgical candidate, or unfit
             for study therapy as assessed by study investigators

          -  Pure sarcomatoid histology

          -  Subjects are excluded if they have an active, known or suspected autoimmune disease.
             Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus,
             residual hypothyroidism due to autoimmune condition only requiring hormone
             replacement, psoriasis not requiring systemic treatment, or conditions not expected to
             recur in the absence of an external trigger.

          -  Subjects are excluded if they have a condition requiring systemic treatment with
             either corticosteroids (> 10 mg daily prednisone equivalents) or other
             immunosuppressive medications within 14 days of study drug administration. Inhaled or
             topical steroids and adrenal replacement doses > 10 mg daily prednisone equivalents
             are permitted in the absence of active autoimmune disease. As there is potential for
             hepatic toxicity with nivolumab or nivolumab/ipilimumab combinations, drugs with a
             predisposition to hepatotoxicity should be used with caution in patients treated with
             nivolumab-containing regimen.

          -  Administration of chemotherapy or any other cancer therapy in the pre-operative
             period.

          -  Subjects with active concurrent malignancies are excluded i.e. cancers other than MPM
             (except non-melanoma skin cancers, cervical dysplasia, and in situ cancers of bladder,
             stomach, breast, colon and cervix).

          -  Subjects with a history of symptomatic interstitial lung disease.

          -  Active systemic infection requiring therapy, as well as positive tests for hepatitis B
             surface antigen or hepatitis C antibody.

          -  Known positive history or positive test for human immunodeficiency virus or Acquired
             Immunodeficiency Syndrome (AIDS).

          -  History of allergy to study drug components.

          -  Women who are pregnant or nursing.

          -  Men with female partners (WOCBP) that are unwilling to use contraception

          -  Prior therapy with an anti-PD1, anti-PD-L1, anti-PD-L2, or anti-CTLA-4 antibody (or
             any other antibody targeting T-cell co-regulatory pathways).

          -  History of any other condition that may require the initiation of anti-tumor necrosis
             factor alpha (TNFα) therapies or other immunosuppressant medications during the study

          -  Underlying medical conditions that, in the Investigator's opinion, will make the
             administration of study drug hazardous or obscure the interpretation of toxicity or
             adverse events.

          -  Prisoners or subjects who are involuntarily incarcerated or compulsorily detained for
             treatment of either a psychiatric or physical (e.g. infectious disease) illness.