This is a single-institution, open-label, early-phase study to assess the ability of ribociclib (LEE011) to inhibit CDK4/CDK6/Rb/E2F signaling and cell proliferation/viability in core and infiltrating tumor tissues obtained from patients with recurrent glioblastoma or anaplastic glioma compared to the baseline/primary pathologic tumor specimen. Abundant preclinical evidence indicates that Rb-deficient cancer cells are resistant to CDK4/6 inhibition and ongoing trials with CDK4/6 inhibitors exclude patients with Rb-deficient tumors. The investigators will evaluate 10 patients with Rb-positive glioblastoma or anaplastic glioma in this study. Given that a minority of glioblastomas ha Rb loss the investigators anticipate enrolling a maximum of 20 patients, to meet our goal of 10 patients with Rb-positive tumors.