As the title suggests my aim in this topic is to make a big list of textbooks on any mathematical topic that take a historical approach. I will start with the ones I know:
Thomas Muir - The theory of Determinants in the Historical order of Development
David M Bressoud - A Radical Approach to Real Analysis
Biggs/Lloyd - Graph Theory, 1736-1936
Some books that have "historical approach" in the title:
Saul Stahl - Real Analysis: A Historical Approach
John J Watkins - Number Theory: A Historical Approach
Hairer/Wanner - Analysis by Its History
W M Priestley - Calculus: A Historical Approach
Winfried Scharlau and Hans Opolka, From Fermat to Minkowski: Lectures on the Theory of Numbers and its Historical Development. From the back cover: "This book is a historically oriented introduction to number theory, including the theory of binary quadratic forms and zeta-functions...."
Harold M Edwards, Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory. "In this book I have attempted to explain the basic techniques and concepts of the theory, and to make them seem natural, manageable, and effective, by tracing their origin and development in the works of some of the great masters...."