What are the application and theories in different branches science?

The Periodic Table of the elements forms the basis of chemistry, the prevailing theory is that each element is primarily distinguished from another by the number of protons in its atomic nucleus.

The primary theory of cosmology is the "big bang" theory. This is not a particularly good name, because it evokes the idea of an explosion, which is not really how it occurred.

Astronomy consists of both the big bang and Subrahamanyan Chandrasekhar's theory of stellar evolution.

The primary theory of geology is plate tectonics.

For biology the key concept is Charles Darwin's theory of evolution.

Isaac newton's method of fluxions (theory of calculus) is probably the key concept in mathematics, much as Euclid's Elements form the basis of geometry.