The reader will find in this article a collection of problems, questions and exer-cises related to the singularities of algebraic and analytic varieties. Many of them are inspired by the work and mathematical conception of Hironaka: they are concrete, involve basic ideas and techniques from geometry and algebra, and they can imme-diately be attacked from scratch. Some problems rely on or use results proven by Hironaka. Simple and double asterisques indicate the more difficult problems; they may potentially serve as a topic of future research.
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