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Special relativity and quantum mechanics fascinate tyros although, a century old by now, their popular image as arcane novelties is exaggerated. This lecture-course teaches how to think about these subjects properly to graduate students and postdocs and beyond from sciences and engineering - not by building oodles of mathematical formalism, but rather through solving surprising problems with elegant tricks of the trade which may amuse even pros. It is designed for those who did not learn SR or QM but wish they had, as well as for those who learnt them but wish they had differently. Everyone is encouraged to attend/audit, and graduate students are automatically permitted to enroll for credit. If undergraduates want to enroll, however, they must pass a test covering basic mathematics plus classical mechanics: contact the instructor within the first 4 days of the quarter (i.e. by January 9th 2025) to arrange a date/time of the test. May be repeated for credit.