(AI) is the domain of producing intelligent machines. ML refers to systems that can assimilate from experience (training data) and Deep Learning (DL) states to systems that learn from experience on large data sets. ML can be considered as a subset of AI. Deep Learning (DL) is ML but useful to large data sets. The figure below roughly encapsulates the relation between AI, ML, and DL:
In summary, DL is a subset of ML & both were the subsets of AI.
Additional Information: ASR (Automatic Speech Recognition) & [NLP](Natural Language Processing) fall under AI and overlay with ML & DL as ML is often utilized for NLP and ASR tasks.