This material is designed to define a "financial system" or "financial systems". The objective is difficult as there is no consensus definition of these terms though they are commonly used.
Definition of Financial System
The OECD defines the term: "A financial system consists of institutional units and markets that interact, typically in a complex manner, for the purpose of mobilising funds for investment, and providing facilities, including payment systems, for the financing of commercial activity."
The IMF defines a financial system: "A financial system consists of institutional units and markets that interact, typically in a complex manner, for the purpose of mobilising funds for investment and providing facilities, including payment systems, for the financing of commercial activity. The role of financial institutions within the system is primarily to intermediate between those that provide funds and those that need funds, and typically involves transforming and managing risk."
Questions Raised

Both definitions are useful starting points, but raise as many questions as they answer. First, both definitions presume a flow of funds, usually regarded as household funds, to satiate the investment needs of productive users of these funds. Second, the model suggests a circular flow, that is, the funds used to support investment are returned to their original source plus a reward, usually an interest rate. Already, the model raises a problem: the fees and charges imposed by the intermediary institution.

Take the current interest rate environment. Banks pay less than 1 percent interest to hold "excess savings" of households and then funnel these funds to productive users at an interest rate spread, let's say 4 percent. Even if we believe that the model works, that is, the funds will increase GDP or produce the next innovation, the only entity making certain money is the financial intermediary - the bank. The premise that it mobilises funds for investment does not state anything specific. The question arises: investment in what? A common refrain is investment in productive enterprise. However, this premise, when subject to deep scrutiny, is so non-specific as to amount to a tautology. In fact, the depositor gets no return when factoring in inflation. The productive user/borrower may get a return - a result set by the market. There is no certainty. Therefore the circular flow model fails.

Second, the model does not account for the emergence of decentralised financial systems dispensing with most financial institutions. Third, that a financial system provides payment facilities states the obvious. What is unstated is that conventional payment systems do not work. When it comes to cross-border payments, the system is effectively broken.

Nevertheless, the financial system is best understood in terms of its utility: payments, moving money from today to tomorrow [investment for the future], moving money from the future to today [lending], and risk management. The financial system, wherever it is, since it is generally country specific, does not perform any utility well, as evidenced by challenger institutions.

LTCM: Example of Entwined Financial Firms Worldwide
Long Term Capital Management [LTCM] "was a highly leveraged hedge fund that as a result of heavy trading in derivatives (securities based on other securities, such as futures contracts, options, and swaps) was entwined with other financial firms all over the world, just like Lehman Brothers." [Richard A. Posner 2009]
LTCM overestimated the diversification of its portfolio. When Russia defaulted on its internal and external debt, an event LTCM did not foresee, investors lost confidence in speculative securities and sought refuge in safe assets. Consequently, LTCM suffered heavy losses rendering it unable to pay is debts when due.
LTCM is illuminating in another as stated by Posner. An "interrelated system of financial intermediaries is inherently unstable" [Posner] Firms that borrow short-term and lend long-term risk a run on its short-term liabilities. The resulting collapse may have "a domino effect on the lenders to it and the borrowers from it and the financial companies with which they are entwined". [Posner] Taking Posner's example, assume A borrows from B [short-term] and lends to C [long-term], and C defaults, B may call its loan, fearing a potential loss. Firms borrow short-term and lend long-term because interest rates generally are lower on short-term borrowings than on long-term borrowings.
Posner introduces another concept called "leverage." Leverage means "borrowing" to increase profits. Suppose a firm has equity of $1 million and no debt makes loans at an annual rate of return of 7%. The firm earns $70,000 per year. Now suppose, that the firm borrows $2 million at 3 percent interest ($60,000 a year) and invests total assets, now $3 million, in similar loans. Seven percent of $3 million is $210,000 per year. After subtracting the cost of $60,000, the annual return is $150,000, more than double its earnings before the borrowing.
However, leverage has a down-side. Suppose the firm has a bad year, in which the return on loans is a negative 5%. In the absence of leverage, the firm loses $50,000, five percent of $1 million. With leverage, it loses $210,000: the loss on the $3 million in loans amounts to $150,000, plus the $60,000 of interest on the borrowed $2 million. A highly leveraged lender has a risky capital structure.

Financial Instruments
Financial instruments are contracts between two or more parties. The diversity of financial instruments is broad. The most common instruments are equity and debt. Equity represents an ownership stake in the issuer; debt represents a claim on the issuer by the creditor. Common equity generally means nothing more than a right to vote [not necessarily the case], a conditional right to dividends, if the Board of Directors declares a dividend, and if all preferred shares are fist paid, a right to sell the instrument, and an expectation of a capital gain. Debt, whether corporate or sovereign, is a claim upon the issuer for repayment of principal and periodic payment of interest payments based on the terms contained in the indenture, the contract underlying the debt instrument.
Preferred equity means a security that, if a dividend is declared, must be paid and the amount of payment reflects an interest rate related to the par value of the security at the time the security was issued. There are two types:cumulative and non-cumulative. Holders of preferred stock may or not have the right to vote and may have the right to convert preferred shares to common equity.