Quote by A. Neumaier;3247879[B
Abstract:[/B] The book fulfils the didactical purpose of showing that
 quantum mechanics and classical mechanics are much more similar than can be seen from the usual presentations of the subject;
 in a very significant sense, theoretical classical and quantum mechanics is nothing but applied Lie algebra;
 quantum mechanics has a common sense interpretation once one takes the thermodynamical findings of statistical mechanics serious in the foundations.

I have positve criticism of your abstract in presentation. Consider me just a reader, trying to understand and see if I am interested in reading further.
I'm a physicist not a philosopher, so I need some added reminder or hint about what didactic means.
 quantum mechanics and classical mechanics are much more similar than can be seen from the usual presentations of the subject;

Give an example with motivational argument to show similarity. Get rid of the () and use standard English.
 in a very significant sense, theoretical classical and quantum mechanics is [sic.: are] nothing but applied Lie algebra;

Again, show by comparison of the usage of Lie algebra's in classical and quantum physics to motivate comparison.
 quantum mechanics has a common sense interpretation once one takes the thermodynamical findings of statistical mechanics serious in the foundations.

This one is a giant step. You need more motivation for making this claim within your abstract. Give a few more details and defer it to the main body of the text using a phrase such as "as will be demonstarted". This should be a good half of your abstract.
I hope this helps on the frontier of written communication.