Can you suggest a book that has a thorough introduction to Singular Value Decomposition?
I find Numerical Linear Algebra by N. Trefreten and D.Bau an extremely wellwritten book. It not only introduces the Singluar value decomposition but explains applications and history. 


Strang's Linear Algebra book linked below is where I learned SVD and it wasn't so bad. I'm sure it's a reasonable intro for one looking to go further. 


This course at Stanford covers singular value decomposition in lectures 1517. The notes are very good, and the lectures are online too. 


The wikipedia page on SVD is pretty good. 


I gave a summary of the section on SVD found in Linear Algebra Done right here: Singular value decomposition over finite fields?. I highly recommend the book. 


Parlett's "The Symmetric Eigenvalue Problem" (since computing the SVD is related to the task of computing the eigensystem of a symmetric positive semidefinite matrix) as well as Stewart's "Matrix Algorithms" were very helpful for me. 

