Hi! Are there any places where I can join swimming classes for adults? Somewhere within a 10 km radius of Palm Jumeirah would be convenient.

Active Sports have adult swim lessons at Dubai International Academy in Emirates Hills.  Supersports also offer adult swimming lessons.  They offer swim lessons in many venues very near the Palm such as Le Meridien Mina Seyahi, Dubai Marina and Emirates Hills but you will need to contact them directly to see which venue offers the adult lessons. Speedo Dubai offer adult lessons at Dubai College, Dubai International Academy and Collegiate American School which are all locations near the Palm.