What Are The Theories That Explain How Countries Grow Economically?

Some of the major theories are -
Classical economics and the quantity theory of money
 Keynesianism
Neoclassical economics

John Keynes is the most significant name that canonized the economic theories regarding nations. While all the details cannot be discussed or enumerated here, I would suggest that you pick up some books on Macroeconomics and Keynes from your library and you will find a wealth of information in them.
Good Luck!

There are different models and theories in economics that are used to measure different characteristics of economic growth. Some of the examples are as follows:
·   Solow–Swan model for measuring total factor productivity
·   Canonical model for measuring rate of technological growth in a country
·   Endogenous Growth theory of economics
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Geographic phenomena and socio-cultural factors theory