Vinoth Raj R teaches a course on digital logic design using Verilog HDL at Velammal Institute of Technology. The course covers various topics related to Verilog including data types, operators, levels of abstraction for modeling circuits, gate-level modeling using primitives, user-defined primitives, data flow modeling, behavioral modeling, and file handling. The emphasis is on modeling, verifying, and synthesizing digital circuits specified in Verilog.