The Garside structure of braids consists of the algebraic properties underlying their decompositions into fractions and the associated normal forms. It turns out that similar structures occur in various different frameworks. The aim of the text is to elaborate a unified theory for such structures, and to apply it to the many situations of algebra, geometry, and low-dimensional topology where such structures are involved.

The current version of the text, which is updated periodically, is freely accessible here: pdf file. Comments and suggestions are welcome.

What is new:
- Corrections (mainly Chapter "Bounded Garside families")
- Chapter "Subcategories", first draft
- Chapter "Self-distributivity", more or less final state ; this has induced a few minor changes in chapters "Preliminaries" and "Bounded Garside families" ; all specific macros in this chapter have names beginning with "\LD", so no conflict can occur with other chapters.

What should be done next:
- Completing Chapter "Subcategories"
- Adapting the end of Chapters "Germs" and "Conjugacy" to the current terminology
- Writing further chapters for Part II: "Braid groups", "Yang-Baxter", "Deligne-Luzstig"