This is one of those books that isn't so much read through as perused. It details Haik-Vantoura's work in deciphering the extra markings of the Masorah Text (the Old Testament) and the discovery that they represented an early (but not simplistic) description of the melodies.
She also explains the process by which the meanings were discovered and verified. It proceeds similarly to the way Egyptian hieroglyphics were decoded, where the verification was in the form of the playing of the melodies that resulted. There are hundreds of excerpts from the Old Testament, illustrating the correct and incorrect interpretations of the symbols.
Haik-Vantoura builds up a syntax, with a description of scales, etc. In short, the symbols below the main text are pitch notation, and the symbols above the text are embellishments. There are also two forms of music: for prose (the narrative portions) and for poetry (psalms, etc). The question of rhythm is answered by the observation that Hebrew is a very rhythmically-oriented language; this, along with the accenting of key words, allows for the rhythm to be reconstructed.
The book provides small examples, but the author has recorded full realizations, which are listed in the back.
The only shortcoming of the book (as someone who is studying algorithmic music composition) is that a grammar of the melodies is not presented, and no one seems to have tackled the problem.