Prologue
The liberation of algebra
The arrival of calculus
Ideas for vectors
Understanding space (and storage)
A surprising new player and a very slow reception
Tait and Maxwell : hatching the electromagnetic vector field
The slow journey from quaternions to vectors
Vector analysis at last
and a "war" over quaternions
From space to space-time : a new twist for vectors
Curving spaces and invariant distances : on the way to tensors
Inventing tensors
and why they matter
Everything comes together : tensors and the general theory of relativity
What happened next
Epilogue.