The Product Design course on Udacity introduces the concept of Design Sprint and its purpose and process. It teaches how to involve stakeholders and differentiate the roles of Product Manager and Designer. The course covers the Understand phase, where lightning talks, interviews, and competitive analysis are used as inputs. It also explains methods like How Might We and Rose Bud Thorn for identifying opportunities and classifying aspects. The Define phase focuses on success metrics, goals, signals, and metrics, as well as crafting Design Principles and writing a Future Press Release. The Sketch phase teaches the Crazy 8's method for brainstorming and creating Solution Sketches. The Decide phase involves creating a Decision Matrix and considering different perspectives. The Prototype phase covers storyboarding, different types of prototyping, and best practices. The Validate phase includes planning and conducting user studies and interviews. The course also emphasizes the benefits of iteration and how to evangelize ideas and create documentation for the engineering team. The course project involves running a Design Sprint, exploring ideas, creating prototypes, conducting user research, refining ideas, and incorporating findings into a final product spec.