The adaptive finite element toolbox ALBERTA has been developed and implemented in conjunction with the Siebert working group (University of Augsburg). This development is on-going. The toolbox provides a common basis for simulations of stationary and time-dependent problems in one, two and three spatial dimensions. Using adapted data structures for geometric, finite element and algebraic information as the basis, abstract adaptive methods, quadrature and grid modification routines etc. are made available in a library. This facilitates a development and programming of applications which is largely dimension-independent. ALBERTA is now used in more than 50 different teaching and research establishments at home and abroad. In the course of the work currently being undertaken to further develop the toolbox, its use on parallel computers is also being progressed, see "Parallel And Adaptive Finite Element Methods".