Please no websites as it only leads to a lot of spam answers from users trying to plug their crappy websites.
There are two schools of analyzing individual stocks: fundamental analysis and technical analysis.
Fundamental analysis studies a company’s financial health through means of dissecting balance sheets, income statements, cashflow statements, and sales projections. The analyst would further perform ratios such as price-to-earnings, price-to-book value, debt-to-equity, etc. to gauge a possible intrinsic underlying value of the company’s stock. There he would decide whether the stock is a worthwhile investment. Books that I would recommend for fundamental analysis would be:
"Value Investing: From Graham to Buffett and Beyond" by Bruce Greenwald
"The Intelligent Investor: The Definitive Book on Value Investing. A Book of Practical Counsel" by Benjamin Graham
On the other hand, technical analysis studies a company’s stock price history to find price patterns and trends that could lead to the stock’s future price action. The analyst would spend hours reading and dissecting daily, weekly, and monthly price charts of individual stocks and general markets. Common terminologies for a technical analyst would be relative price strength, moving averages apply to price and volume, head-and-shoulder patterns, rising wedge patterns, etc. Books that I would recommend for technical analysis would be:
"Secrets For Profiting in Bull and Bear Markets" by Stan Weinstein
"Technical Analysis of Stock Trends" by Robert Edwards
The fun part is deciding which school of thought you would be comfortable with. But honestly, to become a good investor, one must be versed in both. Another book that I would recommend that incorporates both schools would be:
"How to Make Money in Stocks: A Winning System in Good Times and Bad, Fourth Edition" by William O’Neill
Good luck and happy investing!!