libflame contains implementations of many dense linear algebra operations that are provided by the BLAS and LAPACK libraries. (However, not all FLAME implementations support every datatype, and, in many cases, libflame uses a different naming convention for the routines.) The library is a product of the Formal Linear Algebra Methods Environment (FLAME), which encompasses a new notation for expressing algorithms, a methodology for systematic derivation of algorithms, Application Program Interfaces (APIs) for representing the algorithms in code, and tools for mechanical derivation, implementation and analysis of algorithms and implementations.