Finance is a field that reasons about the allocation of assets and liabilities over time under conditions of certainty and uncertainty.
One of the main principles of finance is the time value of money which states - in the absence of inflation/deflation - that the present value of future cash-flows is discounted (or in other words, there is more value of money at present than in the future). Another very important principle is the risk-return tradeoff which says that "more risky projects should have more return" in the efficient economy. Both of these principles are challenged by reality and practice. The era of quantitative easing brought negative interest rates, for instance, in some European countries, while the time value of money assumes positive interest rates. As for the risk-return tradeoff, the definition of risk has more dimensions to it than just typically assumed volatility.
Finance can be broken into three different sub-categories: public finance, corporate finance and personal finance. For more details, see 
Financial economics is the most relevant field for understanding financial markets. In particular, modern portfolio theory and option pricing (Black-Scholes-Merton theory  and its developments) are major achievements of financial economics which allow to make decisions under uncertainty.