The study drug, GSK3326595, is an inhibitor of protein arginine methyltransferase 5 (PRMT5) that potently inhibits tumor growth in vitro and in vivo in animal models. This first time in human (FTIH), open-label, dose escalation study will assess the safety, pharmacokinetics (PK), pharmacodynamics (PD), and preliminary clinical activity of GSK3326595 in subjects with advanced or recurrent solid tumors, as well as clinical activity in subjects with a subset of solid tumors and non-Hodgkin's lymphoma. This is an open-label, repeat-dose, multicenter, 2-part study to establish the maximally tolerated dose (MTD)/ recommended phase 2 dose (RP2D) based on safety and tolerability and preliminary clinical efficacy of orally-administered GSK3326595. Part 1 is a dose-escalation phase to identify the MTD/RP2D based on the safety, PK, and PD profiles observed after oral administration of GSK3326595. This Part will be conducted in adult subjects with relapsed and/or refractory solid tumors. It is estimated that up to 50 subjects will be enrolled into the dose escalation cohort of the study, including up to 38 subjects to identify the MTD and approximately 12 subjects in the PK/PD/metabolite/biomarker expansion cohort(s). Disease-specific expansion cohorts (Part 2) are planned to further explore clinical activity of GSK3326595 in subjects with selected solid tumors and non-Hodgkin's lymphomas. It is estimated that up to 150 subjects will be enrolled in the disease-specific expansion cohorts of the study. The duration of study will depend on recruitment rates and the timing of subjects' duration on study (withdrawal rates due to toxicity or progression), with an approximate duration of 2 years.