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In this monograph, the authors present an introduction to the framework of variational autoencoders (VAEs) that provides a principled method for jointly learning deep latent-variable models and corresponding inference models using stochastic gradient descent. The framework has a wide array of applications from generative modeling, semi-supervised learning to representation learning. The authors expand earlier work and provide the reader with the fine detail on the important topics giving deep insight into the subject for the expert and student alike. Written in a survey-like nature the text serves as a review for those wishing to quickly deepen their knowledge of the topic. An Introduction to Variational Autoencoders provides a quick summary for the of a topic that has become an important tool in modern-day deep learning techniques.