If you believe that you are buying a share of the business when you buy its stock, you have to determine how much the business is worth in order to determine how much the stock is worth..
To do this, you will need to assess company financials in terms of per-share values.
The basis of fundamental analysis is research -- research  to predict stock value that focuses on such determinants as earnings and dividends prospects, expectations for future interest rates, and risk evaluation of the firm.

Value -- an investor needs to know the price and value of a company's stock
The goal of a value investor is to purchase companies at a large discount to their intrinsic value (what the business would be worth if it were sold tomorrow)
Investors will typically focus on the liquidation value of a company or what it might be worth if all of its assets were sold tomorrow -- but not specifically limited to it.   

Growth --  The idea that you should buy stock in companies whose potential for growth in sales and earnings is excellent
This method tends to focus more on the company's value as an ongoing concern.  Overall, the investor will need to look at the underlying quality of the business and the rate at which it is growing in order to analyze whether to buy it.  Investors will buy companies that they believe to be capable of increasing sales, earning, and other important business metrics by a minimum amount each year

Income -- Forgo companies whose shares have the possibility of capital appreciation for high-yielding dividend-paying companies in slow-growth industries
This method focuses on companies that pay high dividends like utilities and real estate investment trusts.  Many times they may invest in companies undergoing significant business problems whose share prices have sunk so low that their dividend yield is consequently very high

GARP -- growth at a reasonable price
This combines value and growth approaches and adds a numerical slant.  It looks for companies with solid growth prospects and current share prices that do not reflect the intrinsic value of the business.  This is highly practiced by Peter Lynch.

Quality -- a hybrid of value, growth, and GARP approaches
This approach looks for high quality businesses selling for "reasonable"  prices.  To do this, the investor must look closely at the company's valuation and at the inherent quality of the company as measured both quantitatively by ROE and qualitatively by the competence of management

Arguments against fundamental analysis
It is based on information that all major participants in publicly traded markets already know, and, therefore, can provide not real advantage.  It is a very subjective method since the meaning of the analysis is often up to the person looking at it to interpret its significance.