NAG Library Mark 25 includes 81 new mathematical and statistical routines. Features include least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression, nearest correlation matrix updates, unscented Kalman filter, change point analysis, high dimensional quadrature using sparse grids, bandwidth reduction of sparse matrix by reverse Cuthill-McKee reordering, solutions to the classical travelling salesman problem and OpenMP utilities. The inherent flexibility of routines in the Library enable it to be used across multiple programming languages, environments and operating systems including C and C++, Excel, Java, Microsoft .NET, Python, MATLAB, Visual Basic and Fortran.