This talk aims to introduce basic concepts from machine learning (ML) and natural language processing (i.e. ML applied to human language) to a non-expert audience. I will try to motivate, present and address the problem of how natural language (human generated text) can be represented and analyzed in a mathematical way. In addition to explaining various fundamental concepts in machine learning (supervised vs unsupervised learning, neural networks, etc), I will introduce and explain the concept of an "embedding space", a powerful and conceptually interesting new approach. Time permitting, I will go further and briefly touch on recent developments such as memory, attention, knowledge and reasoning in the context of neural networks.