This is a list of machine learning libraries that I originally posted on my blog. It is organized by programming language and I tried to list the libraries in order of popularity and available resources.
Python ( Python 2.7 / Python 3.X)
Tensorflow Google's super popular library that reached version 1.0 this year (2017).
PyTorch A great Python library inspired by Torch. It is used a lot in research and is a serious contender to Tensorflow
Keras A higher level abstraction library built on top of Tensorflow
scikit-learn Another high level library geared towards learning.
Jupyter Notebook style workflow with IPython
Java
Deeplearning4j Java deep learning library
Apache OpenNLP Natural Language Processing
C++
Tensorflow C++ API API for C++
MLPACK Scalable ML library
R
I'm not familiar with R myself, but here's some stuff I found:
Introducing: Machine Learning in R
Top 20 R machine learning and data packages