Heinrich weber, lehrbuch der algebra (1895-1896)

As the last important textbook on algebra published in the 19^th century, Weber's Lehrbuch presented a faithful image of algebraic knowledge as then conceived. Although many of the abstract concepts that became central to the structural conception of algebra after 1930 were well known to Weber, they played a relatively secondary role here: algebra was still the discipline of polynomial equations and polynomial forms. The discipline of algebra underwent significant changes between the last third of the 19^th century and the first third of the 20^th century. The problem of finding the roots of polynomial equations dominates a considerable portion of the book Lehrbuch. Like all previous books in algebra, the whole theory of polynomials appears here as conceptually dependent on a thorough knowledge of the properties of the various systems of numbers. All the concepts and techniques related to Galois theory (in particular, the concepts of group and field) are introduced, to a large extent, only as ancillary to that central issue. Research on groups had increasingly focused on questions that are recognized today as structural, and, at the same time, the possibility of abstractly defining the concept had been increasingly acknowledged.