Simply put, a stock is a certificate that represents ownership of a said corporation, and the amount of ownership is based on how many shares one possesses in relation to how many shares are outstanding (i.e. how many shares are present in the market).
While it is a unit of ownership, there are still two main categories of the said ownership. The first one is what people usually buy, the aptly named common stocks. There is also another type called preferred stocks.
Their main difference is two-fold. Common stocks carry voting rights (can vote for who the next CEO or other changes) while preferred stocks have a higher priority in receiving dividends and cash payments in case of bankruptcy, but have no voting privileges. There are other lesser known but equally important types like a convertible preferred share, but the two types discussed are a lot more used.
History of Stocks and their Ownership
Just a brief overview, most academics would put the Roman Republic as the inventor of what we would consider stocks today. The Republic would lease out services to companies, and these companies would issue what they would call a partes which is similar to the listed shares in the stock exchanges and also particulae which are like shares sold outside an exchange.
The earliest joint-stock company would be the English East India Company while the first publicly issuer of shares would be the Dutch East India Company, both of which started in 1600s.
With its long history, shares would have been bought and sold numerous times. If you are interested in tracing the ownership of listed companies in a stock exchange, the easiest way would be to inquire to your broker. There are also more professional sites (of course paid) like Capital Q. What they would require would be the CUSIP number which are nine alphanumeric digits used to identify securities.
If you have a trade ticket number, this could make it a whole easier since you can just search it on Bloomberg or just contact the appropriate exchange and ask them to find it for you.
If all you have is the Ticker i.e. the three or four-letter name of the stock, do not fret as there is still hope. Stock Exchanges and even the company in question should have a list of the current shareholders. You may just need to dig deeper but you will get the list, the question would be the waiting time.