Astronomy and Astrophysics, and cosmology are the most ingenious sub-fields of the physics.
1. Grammatical mistake. "Astronomy, astrophysics, and cosmology". (remove 1 "and")
2. Grammatical mistake. "the most ingenious sub-fields of physics"
3. Consider using "some of the most" instead of "the most". The professor reading this might not agree that his different field is not the most ingenious sub-field.
4. Many good schools have separated astronomy department from physics department.
I admire how the subject uses elegant mathematics and observational data to study the astrophysical phenomenon.
Grammatical inconsistency again. "The subject uses" is singular, but you named three subjects in the previous sentence.
The strong collaborative nature of Astronomy and Astrophysics department of the University of XXX motivates to develop new ideas and work on existing knowledge to understand the solar system and galactic phenomenon in the large-scale universe.
There are too many errors in these two paragraphs alone, it'll be too long to list them all.
My suggestion is to get a good proofreader who can correct your text first, as your English is terrible.