Artificial Intelligence is the broader umbrella under which Machine Learning and Deep Learning come. Deep Learning and Machine Learning are the subset of each other. It's all about tremendous increase in data so results can't be predicted accurate, hence AI comes into the picture and now it is talk of the town. In short Artificial Intelligence is the technique which enables the machine to act as human- beings.
Machine Learning is a subset of Artificial Intelligence technique which uses statistical methods to enable machines to improve with experience.
Deep Learning, we can consider as rocket engine and its fuel as data which feeds the algorithms.
But that doesn't mean it's easy to wrap your mind around. For detail learning check out "HOB Artificial Intelligence"