The document discusses several key concepts in functional programming including: 1) Pure functions that are referentially transparent and have no side effects like modifying variables or data structures. 2) Immutable data and persistent data structures that allow for sharing without synchronization. 3) Separating computational logic from side effects improves modularity and allows for parallelization. 4) A pure functional core can be wrapped with functions that have side effects to push effects to the outer layers.