What actually is a stock market? How is the price of a share or stock decided in the initial public offering, and who decides it?

What is Share Market?
usually, a stock exchange is “a body of people, either incorporated don't seem to be recognized for the purpose of regulation or controlling the business of buying, selling or dealing in securities.”
“Securities refers to shares, bonds, scrip, stocks, debentures stock, and different marketable securities of incorporated companies or similar, government securities, and rights or interest in securities.”
In India, the share market could be a term used to consult with the 2 major stock exchanges within the country— Bombay stock exchange (BSE) , and therefore the National stock exchange of India (NSE). There are 22 regional stock exchanges.
Although the BSE stock price listing has many companies, this index is calculated for the stocks that match to leading companies across a wide range of sectors in the BSE. These shares contribute to more than 50% of the total market capital in the BSE. In this way, a country’s stock exchange index is a fast way to find out and compare the performance of various markets.
An IPO or an Initial Public Offering is the set of stocks that a company sells it for the first time to the public. This is done to expand the capital by going public.
An increase in the IPOs is always a good indication for the economy of a country as it signals more funds into the share market.
During recessions, companies desist from stock trading due to looming losses.