The core logic is that price and value are two different numbers, and the method exists to estimate the second one. The market price is simply what the last willing buyer paid; it says nothing on its own about whether that was a good deal. Fundamental analysis substitutes an analyst's own estimate of intrinsic value, built from the business's fundamentals, for that market price, and then treats any gap between the two as the reason to act, buying when the estimate exceeds the price and avoiding or selling when it does not.
The building blocks are the financial statements and the ratios drawn from them. Revenue and earnings growth, profit margins, debt levels, and cash generation come straight from the income statement, balance sheet, and cash flow statement. Ratios compress those figures into comparable measures: earnings per share turns total profit into a per-share figure, the price-to-earnings ratio restates the share price in terms of that profit, and book value states what the accounting records say the company is worth if its assets were sold and its liabilities paid off. Each of those has its own page, because each is a specific, well-defined number with its own limitations; this page is about what an analyst does with them together, not about any one of them.
The qualitative half of the work often decides the outcome, and it is the part a spreadsheet cannot do. Two companies can show identical numbers on a balance sheet and differ enormously in the durability of their competitive position, the incentives and track record of their management, and the structure of the industry they compete in. An estimate of intrinsic value that ignores those factors is only as good as the numbers it was fed, and a model that looks precise can still be built on a management team that will not execute the plan it describes.
The standing objection to the whole method comes from a different theory of how markets work. The efficient market hypothesis holds that a security's price already reflects available public information, which implies that consistently finding securities the market has mispriced, using only information other market participants also have, is very hard to do. Whether fundamental analysis can reliably produce returns above what a comparable market benchmark delivers, after costs, is a genuinely disputed question rather than a settled one; the case for the efficient market view and the case against it are set out on that page and on the page for alpha, which is the specific measure of whether a result actually reflects skill.
It is regularly paired with, rather than pitted against, technical analysis. An investor might use fundamental analysis to decide which business to own and technical analysis to decide when to buy or sell it; the two study different things (the business versus the trading of its stock) and neither method requires ignoring the other. This page covers only the fundamentals side of that pairing.