LAPACK95 is a Fortran 95 interface to the Fortran 77 LAPACK library. It is relevant for anyone who writes in the Fortran 95 language and needs reliable software for basic numerical linear algebra. It improves upon the original user-interface to the LAPACK package, taking advantage of the considerable simplifications that Fortran 95 allows. LAPACK95 Users' Guide provides an introduction to the design of the LAPACK95 package, a detailed description of its contents, reference manuals for the leading comments of the routines, and example programs.