Inclusion Criteria:

          -  Age >/=18 years to 85 years

          -  Histologically or cytologically confirmed locally advanced or metastatic transitional
             cell carcinoma of the urothelium (including renal pelvis, ureters, urinary bladder,
             urethra). Additional mixed histologies such as squamous, plasmacytoid, adenocarcinoma,
             sarcomatoid, papillary, micropapillary are permitted provided the urothelial cancer is
             the predominant histological component.

          -  Eligible patients must have had either:

               -  Progressed after treatment with at least 1 platinum-containing regimen, (e.g.,
                  ciplatin or carboplatin plus another agent such as gemcitabine, methotrexate,
                  vinblastine, doxorubicin, etc.) for inoperable locally advanced or metastatic
                  urothelial carcinoma or disease recurrence, or

               -  Were ineligible for cisplatin-based chemotherapy, with ineligibility to cisplatin
                  defined by impaired renal function (creatinine clearance < 60 ml/min), a hearing
                  loss of 25 decibels at 2 contiguous frequencies, or grade ≥ 2 peripheral
                  neuropathy or

               -  Locally advanced or metastatic bladder cancer whose disease has progressed within
                  12 months of neoadjuvant or adjuvant chemotherapy.

          -  Biopsy material is required (archival tissue is acceptable if patient could not
             provide fresh or recent biopsy)

          -  ECOG performance status of 0 to 1

          -  Estimated life expectancy ≥3 months

          -  At least one measurable lesion by RECIST version 1.1

          -  Adequate hematologic function defined by white blood cell count ≥3 × 109/L with
             absolute neutrophil count ≥1.5 × 109/L, lymphocyte count ≥ 0.5 × 109/L, platelet count
             ≥100 × 109/L, and hemoglobin ≥9 g/dL (may have been transfused)

          -  Adequate hepatic function defined by a total bilirubin level ≤ the upper limit of
             normal range (ULN), an aspartate aminotransferase (AST) level ≤1.5 × ULN, and an
             alanine aminotransferase (ALT) level ≤1.5 × ULN

          -  Adequate renal function defined by an calculated creatinine clearance > 30 mL/min
             according to the Cockcroft-Gault formula

          -  Both male and female subjects must be willing to use highly effective contraception
             (that is, methods with a failure rate of less than 1% per year) throughout the study
             and for at least 30 days after last avelumab treatment administration if the risk of
             conception exists (see section 6.1.7). [NOTE: The effects of the study treatment on
             the developing human fetus are unknown; thus, women of childbearing potential and men
             must agree to use highly effective contraception, as stipulated in national or local
             guidelines. Should a woman become pregnant or suspect she is pregnant while she or her
             partner is participating in this study, the treating physician should be informed
             immediately.

          -  Signed written informed consent

        Exclusion Criteria:

          -  Concurrent treatment with an anticancer treatment

          -  Prior therapy with any drug targeting T cell coregulatory proteins

          -  Major surgery for any reason within 4 weeks or if the patient had not fully recovered
             within 4 weeks

          -  Concurrent systemic therapy with corticosteroids or other immunosuppressive agents, or
             use of any investigational drug within 28 days before starting trial drug; short-term
             administration of systemic steroids (that is, for allergic reactions or the management
             of immune-mediated adverse events while on study is allowed

          -  Patients with active central nervous metastases will be excluded. Appropriately
             treated CNS metastases with either surgery or radiation therapy are permitted to
             participate in the study

          -  Previous malignant disease (other than urothelial carcinoma) within the last 5 years,
             with the exclusion of basal or squamous cell carcinoma of the skin, cervical carcinoma
             in situ and prostate adenocarcinoma with Gleason score 6-7, pT2b.

          -  Prior organ transplantation, including allogenic stem-cell transplantation

          -  Known history of testing positive for HIV/AIDS, HBV, or HCV (including acute and
             chronic infection)

          -  Active or history of any autoimmune disease or immune-deficiencies (patients with type
             1 diabetes, vitiligo, psoriasis, hypo- or hyperthyroid disease not requiring
             immunosuppressive treatment are eligible)

          -  Known monoclonal antibody hypersensitivity, history of anaphylaxis, or uncontrolled
             asthma

          -  Persisting toxicity related to prior therapy that was > grade 1 according to NCI-CTCAE
             v4.0; grade ≤2 sensory neuropathy is allowed

          -  Pregnancy or lactation

          -  Clinically significant (i.e., active) cardiovascular disease: cerebral vascular
             accident/stroke (< 6 months prior to enrollment), myocardial infarction (< 6 months
             prior to enrollment), unstable angina, congestive heart failure (≥ New York Heart
             Association Classification Class II), or serious cardiac arrhythmia requiring
             medication All other significant diseases, which in the investigator's opinion may
             influence the patient's tolerance of trial treatment. Other severe acute or chronic
             medical conditions including immune colitis, inflammatory bowel disease, immune
             pneumonitis, pulmonary fibrosis or psychiatric conditions including recent (within the
             past year) or active suicidal ideation or behavior; or laboratory abnormalities that
             may increase the risk associated with study participation or study treatment
             administration or may interfere with the interpretation of study results and, in the
             judgment of the investigator, would make the patient inappropriate for entry into this
             study

          -  Legal incapacity or limited legal capacity, including any psychiatric condition that
             would prohibit the understanding or rendering of informed consent

          -  Vaccination within 4 weeks of the first dose of Avelumab and while on study was
             prohibited except for administration of inactivated vaccines (e.g., inactivated
             influenza vaccines)