I read really good things about Eigen and was interested to know if it can be used with gfortran (either Windows or Linux).
If yes, how to call Eigen routines inside a Fortran program? Can someone give an exmaple Fortran program calling Eigen, probably solving Ax = b system.

Many thanks in advance for help.

You can use a very small subset through its BLAS and Lapack interface but then better use the standard Lapack library and an optimized BLAS like Eigen, OpenBlas or Atlas.