The thesis develops a competitive compositional semantic parser for Abstract Meaning Representation (AMR). This approach combines a neural model with mechanisms that echo ideas from compositional semantic construction in a new, simple dependency structure. The thesis first tackles the task of generating structured training data necessary for a compositional approach, by developing the linguistically motivated AM algebra. Encoding the terms over the AM algebra as dependency trees yields a simple semantic parsing model where neural tagging and dependency models predict interpretable, meaningful operations that construct the AMR.