Joe Celko walks us through key and less-key normal forms:
Even before RDBMS, we had network and hierarchical databases. Their first goal was to remove redundancy. We want to store one fact, one way, one place, and one time. Normalization goes a step further. The goal of normalization is to prevent anomalies in the data. An anomaly could be an insertion anomaly, update anomaly, or deletion anomaly. This means that doing one of those basic operations destroys a fact or creates a falsehood.
It’s an interesting read on a sadly-neglected topic.