The financial markets comprise many interlocking markets in different financial instruments. These are the basic ones:
Shares: A share is a tradeable certificate of part-ownership of a company listed on a stock exchange. A shareholder owns a part of the company, is entitled to vote in its annual general meetings (in proportion to the number of their shares) and is entitled to a portion of the company's profits (a "dividend"). Shares are also known as stocks or equities.
Bonds: A bond is a tradeable certificate of debt which guarantees the bondholder an interest payment (a "yield") when the time limit on the bond expires (when it "matures"). Bonds can be sovereign (government debt) or corporate, long or short term, investment-grade (low risk, low return) or junk (high risk, high return). The king of all bonds is the Treasury bond, issued by the US Federal Reserve.
Foreign exchange: The oldest form of financial market transaction is the buying and selling of national currencies one for the other. Originally, forex transactions were to fund purchases of goods and services; now forex markets are the major venue for speculation, dwarfing all others.
Derivatives: The collective name for futures, options and swaps, as they are all "derived" from more basic instruments, such as stocks, bonds or commodities. Derivatives can either be standardised and regulated and sold on exchanges, or over the counter ("OTC"), and completely unregulated.
Futures: A future is a tradeable agreement to buy or sell a particular amount of a particular commodity (whether US dollars or pork bellies) at a particular time.
Swaps: A swap is a tradeable package of parts of two different cash flows, which don't involve trading the underlying asset. Swaps are of two basic types: "interest-rate swaps" (where counter-parties swap floating for fixed interest rate payments) and "currency swaps" (where counter-parties swap interest payments in two different currencies).
Options: An option is the right, but not the obligation, to buy or sell an underlying asset, whether a bond or a stock or whatever, within a certain period. Options can either be "call" options (the right to buy) or "put" options (the right to sell).
There are constant new financial "innovations" being invented, bought and sold — in large part in an effort to avoid regulation.