What is equity analysis and equity investment process?

Equity analysis, is taking the financial statements of the company and figuring out important financial ratios which give an indication of the strength of the company. There are many ratios, but some are
P/E (price to earnings) ROC (return on capital) P/S (price to sales) Price per share, Profit before interest and taxes. Dividend per share. Lots of things like this. If you know what to look for This is a good form of Rating a company

Equity investment process is more difficult to understand what you are looking for with this question.

A company makes itself into millions of tiny parts called shares, some of these shares, it sells on the open market to bring in Capital (money) for the company to do things with, hopefully to make the company more profitable ( these are issued shares)
millions of shares are held back in the company, but are not included as part of the company until they are issued (sold on the market, or excercised as options to insiders)

An investor either signs up for a public offering to buy shares, if he likes the company, or he buys share on the stock exchange at the market price when they trade.

Profits of the company are either kept in the company to finance growth or are paid to the shareholders as dividends (or a combination of both) Each issued share of a series are entitled to the same amount of dividend, no matter what was paid for the underlying share. Shares can also increase or decrease in value depending on what others feel they are willing to pay to buy your shares

That is as good As I can figure out your question