Historical textbook on group theory/algebra

I found the book The genesis of the abstract group concept, by Hans Wussing, to be very interesting. It gives a scholarly history of the development of the concept of group, from its roots in number theory, geometry, and the theory of equations prior to the 19th century, through to (more-or-less) the end of the 19th century.

As for reading the original papers, while there is a lot to be said for this, you should bear in mind that these are not only typically written in languages other than English, but are also in a mathematical language that is quite different from our modern language. If you do decide to look at the originals, Wussing's book would be a good guide to the major papers in the initial development of group theory.

Please allow me to quote from Joseph Rotman's book "Galois Theory", as follows

"When writing the definition of Galois group for this text, I asked myself an obvious question: how did such thoughts occur to Galois in the late 1820's? The answer, of course, is that he did not think in such terms; for its first century, 1830-1930, the Galois group was a froup of permutations. In the late 1920's, E.Artin, developing ideas of E.Noether going back at least to Dedekind, recognized that it is both more elegant and more fruitful to describe Galois groups in terms of field automorphisms(Artin's version is isomorphic to the original version). In 1930, van der Waerden incorporated much of Artin's viewpoint into his influential text "Moderne Algebra," and a decade later Artin published his own lectures. So successful have Artin's ideas proved to be that they have vertually eclipsed earlier expositions. But we have lost the inevitability of the definition; group theory is imposed on the study of polynomials rather arising naturally from it. This appendix is an attempt to remedy this pedagogical problem by telling the story of what happened in the beginning. The reader interested in a more thorough account may read [Edwards] or [Tignol] "

H.M.Edwards, Galois Theory,Springer,1984

J.-P.Tignol, Galois Theory of Algenraic Euqations, Wiley, 1988

Unknown Quantity by John Derbyshire is an excellent historical account of the evolution of abstract algebra. The book is aimed at the "mathematically inclined" and covers the history of algebra from birth to present day (or pretty close.)