This is partial list of the main textbooks containing explanations about most of the methods implemented in the Atlas package.
S. Kobayashi, K. Nomizu "Foundations of differential geometry" - N.Y.: John Wiley and Sons, V. 1, 1963; V. 2, 1969.
B. A. Dubrovin, S. P. Novikov, A. T. Fomenko "Modern geometry. Methods and applications." -M.: Nauka 1986.
P.K. Rashevsky "Riemannian Geometry and Tensor Analysis" -M.: Nauka 1967.
Arthur L. Besse "Einstein Manifolds" Springer-Verlag Berlin Heidelberg V. 1-2 1987.
S. Chandrasekhar "The mathematical theory of black holes" - N. Y.: Oxford University Press V. 1-2 1983 .