The Livermore Big Artificial Neural Network toolkit (LBANN) is an open-source, HPC-centric, deep learning training framework that is optimized to compose multiple levels of parallelism. LBANN provides model-parallel acceleration through domain decomposition to optimize for strong scaling of network training. It also allows for composition of model-parallelism with both data parallelism and ensemble training methods for training large neural networks with massive amounts of data. LBANN is able to advantage of tightly-coupled accelerators, low-latency high-bandwidth networking, and high-bandwidth parallel file systems. LBANN supports state-of-the-art training algorithms such as unsupervised, self-supervised, and adversarial (GAN) training methods in addition to traditional supervised learning.