We explore incremental assimilation of new knowledge by sequential learning. Of particular interest is how a network of many knowledge layers can be constructed in an on-line manner, such that the learned units represent building blocks of knowledge that serve to compress the overall representation and facilitate transfer. We motivate the need for many layers of knowledge, and we advocate sequential learning as an avenue for promoting the construction of layered knowledge structures. Finally, our novel STL algorithm demonstrates a method for simultaneously acquiring and organizing a collection of concepts and functions as a network from a stream of unstructured information.