Devoted to the theory of topological higher Franz-Reidemeister torsion in $K$-theory, this book defines the higher Franz-Reidemeister torsion based on Volodin's $K$-theory and Borel's regulator map. It studies the relation between the higher Franz-Reidemeister torsion and other torsions used in $K$-theory: Whitehead torsion and Ray-Singer torsion.