Finance is the study of money and how it is used. Specifically, it deals with the questions of how an individual, company or government acquires the money needed - called capital in the company context - and how they then spend or invest that money. Finance is, correspondingly, often split into three areas: personal finance, corporate finance and public finance.
At the same time, finance is about the overall "system"  - i.e. the financial markets that allow the flow of money, via investments and other financial instruments, between and within these areas; this "flow" is facilitated by the financial services sector. A major focus within finance is thus investment management — called money management for individuals, and asset management for institutions — and finance then includes the associated activities of securities trading, investment banking, financial engineering, and risk management.
More abstractly, finance is concerned with the investment and deployment of assets and liabilities over "space and time": i.e. it is about performing valuation and asset allocation today, based on risk and uncertainty re future outcomes, incorporating the time value of money (determining the present value of these future values, "discounting", requires a risk-appropriate discount rate). As an academic field, finance theory is studied and developed within the disciplines of management, (financial) economics, accountancy and applied mathematics. Correspondingly, given its wide application, there are several related professional qualifications, that can lead to the field. As the debate to whether finance is an art or a science is still open, there have been recent efforts to organize a list of unsolved problems in finance.