What is this growth on my
azalea leaves?

This is azalea leaf gall. It is a fungus that does not hurt the azalea, but it does look unsightly and will slowly become more and more frequent making the plant look bad. The best way to control it is to pick off infected leaves and throw them away. Over time the number of infected leaves will be reduced.

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Related Resources:
Exobasidium Leaf and Flower Galls (Azalea Leaf Gall & Camellia Leaf Gall)
Azalea: Leaf and flower gall