Algebraic symbolic and numeric methods -- Basics of ring theory -- Basics of polynomial theory -- Groebner basis -- Polynomial resultants -- Linear homotpy -- Solutions of Overdetermined Systems -- Extended Newton-Raphson method -- Procrustes solution -- Applications to geodesy and geoinformatics -- LPS-GNSS orientations and vertical deflections -- Cartesian to ellipsoidal mapping -- Positioning by ranging -- Positioning by resection methods -- Positioning by intersection methods -- GNSS environmental monitoring -- Algebraic diagnosis of outliers -- Datum transformation problems.

The book presents modern and efficient methods for solving Geodetic and Geoinformatics algebraic problems. Numerous examples are illustrated with Mathematica using the computer algebra techniques of Ring, Polynomials, Groebner basis, Resultants (including Dixon resultants), Gauss-Jacobi combinatorial and Procrustes algorithms, as well as homotopy methods. While these problems are traditionally solved by approximate methods, this book presents alternative algebraic techniques based on computer algebra tools. ¬ This new approach meets such modern challenges as resection by laser techniques, solution of orientation in Robotics, transformation and bundle block adjustment in Geoinformatics, densification of Engineering networks, analytical solution for GNSS-meteorology and many other problems. For Mathematicians, the book provides some practical examples of the application of abstract algebra and multidimensional scaling.