During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software. The book is accompanied by a full distribution of ALBERTA (Version 1.2) on a CD including an implementation of several model problems. System requirements for ALBERTA are a Unix/Linux environment with C and FORTRAN Compilers, OpenGL graphics and GNU make. These model implementations serve as a basis for students and researchers for the implementation of their own research projects within ALBERTA.