A very concise introduction and presentation of the inner product and Hilbert spaces, the Schwarz inequality theorem with proof, Bessel's inequality, as well as several other basic theorems. A quite useful, practical summary.
http://www.math.umn.edu/~jodeit/course/Hilbert.pdf
Rights:
open access:
http://www.math.umn.edu/~jodeit/course/Hilbert.pdf
