Historical textbook on group theory/algebra Recently I have started reading about some of the history of mathematics in order to better understand things.
A lot of ideas in algebra come from trying to understand the problem of finding solutions to polynomials in terms of radicals, which is solved by the Abel-Ruffini theorem and Galois theory.
I was wondering if there's a textbook (or history book which emphasizes the mathematics) that goes vaguely in chronological order or explicitly presents theorems and concepts in their historical context.
Alternatively, if you think it would be better to attempt to read the original papers (Abel's famous quote about reading the masters comes to mind), such as the works of the mathematicians mentioned in this wikipedia article , how would I go about doing so?
EDIT: while researching some of the recommended books, I found  this interesting list (pdf)  of references.

The inspiration for this question came from asking myself "why would someone bother/think of defining a normal subgroup in the first place?" (although I already know the answer) and hence I am asking about Galois theory, but really this question works for any area of mathematics and perhaps someone should open a community wiki question for that.

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.)  
