TensorFlow is a library for neural networks and, mainly, deep learning developed by Google.
Installations instructions can be found here.
Premade estimators in TensorFlow
To make things a bit easier, TensorFlow has some premade estimators (classifiers) that you can use directly without bothering about defining all layers in your model. A guide can be found here.
MNIST in TensorFlow
Note that the deep ConvNet takes a substantial amount of time to train and evaluate, around 10 minutes for 5000 iteration steps on a fairly fast laptop.