Tensorflow is, of course, Google's well-known neural network framework. This is a free and open source framework that is usable with Python and C++, and has been available to the general public since 2015.
Tutorials on Tensorflow are available from Google here: https://www.tensorflow.org/tutorials/.
Keras is a higher level library that provides a more user-friendly interface to Tensorflow, which was originally written by Google Brain's Francois Chollet. Readers may actually consider starting with Keras before moving on to Tensorflow.
Information on Keras is available here: https://keras.io/.