PostgreSQL is the open source database started at UC-Berkeley back in 1986 as Postgres project. Today, PostgreSQL is an enterprise class RDBMS, one of the most powerful database engines available.
PostgreSQL includes the ability to use various programming languages including PERL, Python, R, and many others. It also allows several additional modules to add features and capabilities.
PostgreSQL is available under a liberal open source license. From the project website:
[The] license gives you the freedom to use, modify and distribute PostgreSQL in any form you like, open or closed source. Any modifications, enhancements, or changes you make are yours to do with as you please.