Network: objects consisting of modules which communicate via connections which may have adjustable parameters themselves. The network is itself a module.
Connections: objects that connect the layers of modules in the network.
Trainer: an object that uses a dataset to adjust the free parameters of the network.
Dataset: a set, typically very large, of inputs and desired outputs.
More to the concepts
How this encourages me
Brief question: Does anyone remember linear algebra? I need a refresher. Guess it's time for Khan Academy.