Jacques Darne, Universite de Picardie Jules Verne, Amiens, France. Martin Palmer, Institutul de Matematica Simion Stoilow al Academiei Romane, Bucure\cb{s}ti, Romania. Arthur Soulie, Normandie Universite, Caen, France.

Description
Chapters Introduction 1. General recollections 2. Strategy and first examples 3. Partitioned braids 4. Virtual and welded braids 5. Variants on partitioned welded braids 6. Braids on surfaces A. Some calculations of lower central series B. Presentation of an extension