Artificial Intelligence (A.I.)
A field of study with the goal of creating machines that exhibit intelligence. It is the Broad way of all the things in the ML and DL. So basically AI is a broad field of study over all ML, NLP and DL. Machine Learning is a particular sub-field of AI that concerns itself with the use of data to train algorithms to perform challenging tasks where the rules are complex or difficult to fully specify the algorithm to complete a task. NLP is a sub-field of AI that studies the use of algorithms to understand natural language with the use of complex algorithms. Machine Learning is majorly used in Natural Learning Programming. Deep Learning is a class of machine learning algorithms so its a sub class of AI.
Machine Learning (ML)
Machine Learning is a sub-field of Artificial Intelligence(A.I.), which focusses on the use data to train computer algorithms to perform Different tasks that typically cannot be done through simple algorithms (or very difficult to accomplish through it) through hard wiring programs and the logics into a program, because no one is quite sure what are the specific rules. Like Recognizing objects in images is one such task where the rules are unclear complex and unclear.
Note that ArtificiaI Intelligence, unlike Machine Learning, need not require the use of data as specified. So as long as you can convince the user that your system exhibits intelligence, anything goes and works fine. It may also be unclear what the rules are. And even if we can hand code the rules, it is a huge pain to have to craft them for different domains and applications, hence the huge shift towards using ML algorithms in solving AI tasks.
Natural Language Processing (NLP)
A sub-field of AI where ML algorithms are heavily used to make sense of natural languages, for e.g., by figuring out the subject of a sentence, or to translate sentences from one language to another.
Even though a typical language comes with rules, i.e., grammar, different languages have different grammar, and each of them often have exceptions to the rules. Furthermore, sentences often can be ambiguous if one does not take into account the context in which it was written, or if one is unaware of some prior knowledge necessary for understanding the sentence. Hence, hard wiring grammar rules into a program is often insufficient for it to perform an NLP task such as machine translation, well.
A class of machine learning algorithms that are (very) loosely biologically inspired. For example the Convolutional Neural Network (CNN), Long-Short Term Memory (LSTM) network, are deep learning algorithms. You train them using data, just like you would any machine learning algorithm. CNNs are typically used in computer vision tasks such as object recognition or detection, and LSTMs are commonly used for performing NLP tasks such as sentiment analysis, machine translation, or part-of-speech tagging.