I've read over 40 books on this area of mathematics cover to cover, and Tignol's stands out as best for several important reasons –
- most comprehensive, covering quadratic equations in ancient times contrasted to middle ages, Renaissance, 17th century symbolic algebra all the way through Galois Theory, with appendices on modern ways of seeing Galois' work.
- Cleanest, most focused path through the topic
- Clearest exposition, easiest to follow and understand
- best use of historical information and placement of that information
- math is a relay race, with the baton handed from one creative mind to another; Tignol does the best job of illustrating this handoff. His exposition of contributions by Lagrange and Vandermonde is exemplary and unique